Thus far, this has in my saga only been used at the Hermetic Tournament.
What have others used it for? It seems I should likely have this turn up more often...
Vrylakos
One of my players has a chracter named Louis ex Flambeau. At the time of this adventure, she was about 12 years out of Gauntlet. The character has Skilled Parens and has built up a small positive bit of House Acclaim and Reputation.
At Tribunal, a young Flambeau (either near gauntlet or just past it; I forget which) approached him. He asked Louis "Will you do me the honor of a Certamen match in the School of the Founder?" (Creo Ignem is Louis' study). The apprentice fully expected to be clobbered, but considered it a mark of honor to be beaten by a powerful Flambeau after a respectably long Certamen. It was effectively a self-determined hazing. The young Flambeau's friends cheered both Louis and their friend.
In terms of actual use as a dispute mechanism, none yet.
If you have any trouble-making PC's, it's a natural, even between players.
If not, then it falls to NPC's to open that particular door. I've seen Certamen used to introduce Hermetic "antagonists", NPC's who are not quite "villains" but whose political/personal plans either conflict with or threaten the PC's and/or their Covenant.
Certamen means "duel", so any classic excuse for a duel is fair game to use it in your saga. Difference of opinion, insult intentional or imagined, pursuing the same object of desire (whether a political position, item or person), or just someone who "you just seem to rub the wrong way".
As defined, it's also a weapon for the more politically savy. If any vote is upcoming, Certamen can be used directly or indirectly to influence that - directly by demanding the loser to vote a certain way, but indirectly to take the loser out of the vote for the time one way or another, either by removing them from the area (for votes that they cannot predict, and so most likely won't think to pass on their sigil) or by pressuring them (an "if/then" situation that discourages participation).
Many Players don't like to initiate this sort of conflict, so the idea that "it's better than a wizard's war" is another consideration if you want to push them to be the aggressor.
While Tribunals are always the predictable environment, there are many other times when two magi meet and can have a disagreement, or a grudge or rivalry, or just conflicting goals where one could use Certamen to resolve the situation.
Tremere, esp, are good at this sort of "playing the long game". A Tytalus would also do it, perhaps with something not so important, just to teach some naive sodalis how that game is played, for their own betterment. Flambeaux could have an urgent martial goal and force assistance, Bonisagus could argue over rights to an apprentice or a valued study resource - the list is endless.
On a meta-level, I planned a Certamen into the first play session of our current saga as a way to introduce combat-like mechanics with a situation that didn't really hold that much downside in the event of a loss. (It didn't hurt that our troupe's newest player's magus was in fact ex Tremere....) The in-game rationale was to determine who held the position of covenant council chair - basically a position of some minor prestige, and also the tie-breaking vote on covenant decisions.
I have found certamen to be utterly unbalanced, and no way to resolve disputes--no one would actually challenge you to a certamen they had any hope of losing. The one time I made the mistake of agreeing to a certamen match, another player just used it to rob me of my private vis source (I don't recall why I even accepted, but I believe the storyguide implied I had to for some reason), as I had two strong techniques and one strong form, and ended up getting no good arts into the mix. Since anyone who focuses on certamen has a better art distribution for the contests, as well as a huge bonus for tremere, you'd basically have to be mad to accept a challenge,have to hire a tremere to defend you, be mad to hire a tremere to do this for you. . . all the players I have played with since have seemed to agree, and there has never been another certamen match in any saga I have played in, except as a demonstration or friendly match (there has never been another Tremere, either. . .).
Certamen is one of those relics of older editions that needs to get thoroughly revised or get thrown out.
If it was a personal vis source (as per the Virtue) or one that had been recognized as yours in any kind of Tribunal ruling, then I believe he just did not have the right to challenge you for it, because that would be "depriving a member of his magical power". If it was just something that you found and kept for yourself, I suppose he would have the right...
As I understand it, while certamen does have a legal standing in the Order, it is strictly within the context of a legitimate dispute. If there is no dispute (for instance, you already had a ruling go your way on the subject), there can be no challenge. Of course, that still leaves the door open to abuse, except...
Why didn't you just tell him something like
"allow me to answer that challenge with a declaration of Wizard War ?"
Not convinced there is anything that 'forces' a magus to accept certamen... of course, you probably want to avoid a reputation as a coward, or might not want your dispute resolved by tribunal, but I don't think it is a method that guarantees compliance for the 'bully'.
There are always plenty of reasons to choose to accept a challenge, but an utterly unreasonable challegne can still be responded to by the universal symbol of the clenched fist with central finger in the errect position.
Bulying by certamen only works if the alternatives are worse, or the victim is especially weak willed.
The most substantial thing it has been used for in our current saga is who gets to eat a magical fish. We catch the fish every 7 years and the eater can speak to all animals. There was no clear agreement so each time a fish turned up we fought a Certeman to decide who got it
I have had Certeman pop up a few times in fifth edition, and it usually has interesting and important results...
In Light of Andorra
- At Barcelona, Erat Caecus (npc) challenged Inigo Xalbador (pc) to Certamen in an attempt to take over leadership of their expedition. Erat was favored to win, as he was much older and was using vis. But the dice went against him, and he lost. He was banished from Barcelona and forbidden to interfere with the expedition (which he did anyway).
- Later on, when Valentino first came to Andorra (pc), he challenged Archmagus Antonio (npc) to Certamen for sport. We got to play with the Vertamen Schools, he was using Hoplomacus and I was using Inirelte's Certamen (a school I invented for my game). Valentino lost, as he knew he would, but he made an excellent showing and that was the whole point.
- Most recently, Inigo and Octavian had a duel. Octavian was leaving the game, but he wanted to exit on a high note with drama and flare. Inigo wanted some lab texts Octavian had in his posession (recovered from the earlier expedition). Octavian didn't want to give them up voluntarilly, and his counter condition was he wanted to take Inigo's apprentics (who is also Inigo's daughter). The fight was on, and it looked like the odds were slightly in Octavian's favor. The initiative was his, me makes his roll...
...and he botched it. Certamen lost, throwing a wet blanked on the dramatic exit.
In another game, LadyP's table top, I lost some important certamen against another player and as a result I had to assist them in the lab for a season. I show up for my first day of work, the guy's lab is a smelly hovel, so I cast a spell to freshen the air. The guy goes nuts on me and tries to stab me with poison daggers. I "wizard leap" out of the way, decide not to kill him, and leave. I felt that his attempt to kill me nullifies my obligation to work for him for a season. The council was in the middle of hashing that out, when LadyP's Bonisagus maga pullls out a twist. She challenges the stinky-mage to certamen, beats him, and takes his assistant (me) away from him for the season. So I go along with it, figuring that her lab is much cleaner and that I can figure out where she hides her la texts. 
There have been a lot of classic Certamen battles over the years. My old ArM4 Jerbiton magus, he just could not win at certamen, no matter what he did! No special flaws or disadvantages or anything, the dice just were aginst that character every single time he was in a clutch.
We just had a perfect example of what certamen is used for in my game - a Criamon had insulted the covenant red cap/autocrat to the point that said red cap was leaving. The remaining magi of the covenant was rather upset by this (they considered the redcap a friend), so they challenged the criamon to a certamen to get him to go and apologize before it was too late.
The criamon beat the first challenger pretty easily, but was taken down by the second maga. As it became a matter of pride, the criamon was willing to spend 8 pawns of vim vis on the duel - and both sides ended up using several points of confidence.
If he had been able to, I am pretty sure he'd avoided the duels - but since that is the same as conceding, he figured he would be better served by his magic.
What was the "symetrical" result if he had won? Would the rest of the covenant had to have taunted the RC as he left? 
It was the first time I had ever played out a certamen, a decade ago, in 4th edition, and I shouldn't have accepted. That said, even in fifth edition, knowing what I know now, I still have trouble seeing how it could be a reasonable way of resolving disputes, as it is so stilted that you would almost never challenge someone fairly, so no one should generally accept. I mean, why would anyone ever accept a certamen challenge from a tremere? you'd have to be daft, and if it is important, declare wizard's war over it or find some other form of resolution.
All magi have their weaknesses. Generally 10 points worth of flaws in them. Find out hat they are and a Tremere might not be so difficult to beat.
Much can be achieved by the judicious use of knowledge about your opponent, especially when combined with a cunning use of your veto. Tremere are not born into the world with art scores of 5 across the board. Doubling zero is hardly an advanatge.
Who would accept a challenge to certamen over something important against a Tremere that is better than themselves... few I guess. Worse than themselves... most. Equivalent... accepting with some reluctance.
If you don't like the outcome of the certamen you can still declare a wizard war.
If you dont like the outcome because it is unfair then take it to tribunal.
If you don't think the challenge is fair then inform a queasitor - bullying through certamen is a low crime. (core)
You can always convince your dad/big uncle/angry mother or other more talented assocated ot challenge the victorious magus to certamen under the same terms.
The victorious magus is still bound by the code. The restriction 'depriving a magus of his magic' is a pretty all encompassing phrase that would cover most reasons for having certamen in the first place. A losing magus can still obtain the services of a gifted hermetic lawmaster to get his 'stuff' back, perhaps even being compensated in the process.
If you are a one trick pony with all his arts in 2 techniques and one form, well, time to start feeling the the pain of some of those choices. Yeah Tremere is going to hammer you every time if he makes even cursory enquiries into your character.
Certamen is a political device and as such is far from an absolute. I love anything like that because it explains the escalation of dispute in cases where people are aggreived. The outcomes may be binding but there are plenty more steps in the chain for you to advance the dispute with.
I like the idea of Certamen, and currently play a Tremere. Although Certamen has never really been used much in my sagas.
I wish for some opportunities to use it though, to deal with political issues and eprsonal disputes. I see the problem as to why everyone else would be playing Tremere's game - which they have an advantage in. But those things aside, Certamen is an accepted way for resolving differences.
In the saga where I play a Tremere we have Tribunal coming up. And I'm looking for opportunities to flex my certamen-muscles. But for what? If I'm going to force my covenant-mates into voting for issues to help house Tremere - well I might not become more popular. Not too vital.
But since a Certamen is a quid pro quo, and I challenge a magus, wanting him to vote a certain way, what would he be entitled to if he wins (god forbid that)? He can't demand that I vote a certain way, since Tremere do block voting, and the regional boss controls my sigil.
Research your target - don't just pick one at random.
What does your target want?
If he'll vote your way for a tiny bribe anyway the certamen might well be overkill though.
Yes. But that doesn't satisfy my need to assert myself as an able duellist. And that only works for issues he is indifferent about. To make the humiliation total, it'll be an issue important to him, or something his house-mates will resent him doing.
Also, there is a Mercere PC magus that I'm at odds with, so...
Go to the tournament at Castra Solis, or just hang around other Tremere magi and get involved in a lot of public 'practice'.
Certamen is like nuclear weapons for me. Knowing that someone is able to win against me makes me treat him more carefully.
Using it becomes unnecessary just because it exists.
We use Certamen quite a lot in our 3rd edition Saga (we haven't been playing 5th edition long enough for it to have come up yet). We have a Peripheral Code ruling that if a Magus refuses a Certamen challenge, then they are deemed to have lost by default, and the victory conditions still apply. Magi, as a consequence, must be very careful who they offend. This is balanced by very strict criteria of what can count as legally enforcable victory conditions, by the no-second-challenge rule, and by anti-bullying precedents.
Yes, Certamen (in-game) is unfair, but that's just the way things are in the community of Wizards - some are simply massively more powerful than others.
You are right that you are usually slightly mad to accept a certamen challenge from much more senior magus. But, certamen between magi of roughly equal age is not usually a foregone conclusion. As others have commented, most magi have weak points in their knowledge of Arts --- even archmagi are likely to be relatively poor in a few (or even many Arts).
Tremere certainly don't always win in Certamen --- doubling a very low Art Score is still going to lead to a low certamen attack/defense total.
Certamen is useful because there are heaps of things that are worth arguing about, that are not worth killing for or dying over (i.e. declaring Wizard War).
Also, remember it is possible for a character to call upon a Certamen champion. So, challenging a much weaker opponent to Certamen does open you to the risk of actually needing to fight a much stronger opponent.