Societates describes magi who fights in the School of Ramius, i.e. uses magic for defense while swinging a mundane sword that bypasses Parma. The description in the book says that students of this school tend to focus on their own Parma, trusting it to protect them while they engage in melee.
If their Parma does not protect their weapons, then a very easy counter to this fighting style would be to attack the weapon directly, either destroying it with Fist of Shattering (level 15 PeTe, with the extra magnitude for affecting metal), or ripping the sword out of their hands with Disarm the Warrior (level 20 ReTe), or simply mastering Wizard's Parry (level 5 ReTe) and fast casting it every round. Wizard's Parry is a low enough level spell that most people could reliably spont it.
If, however, Parma does protect a held weapon, then unless you're a Terram specialist there's very little you can do to counter the School of Ramius other than get a suit of armor and raise their Defense and Soak as high as they can. So it seems that melee magi are either extremely overpowered or extremely underpowered depending on this ruling.
The book says that Parma protects "the maga, her clothing, and other items that are very close to her" (Ars p85), but it's not clear whether that includes objects that the magus is holding, or if a four-foot long sword qualifies as "very near" at all. Googling hasn't been much help.
Normally Parma Magica would not cover any decent-sized weapons. (Cesti and similar ought to be covered, I would think.) Yes, the weapons are vulnerable. But you could use counter magic against their magic without having to penetrate. Parma Magica does cover talismans being held, though, which can easily create an exception for a shield or sword or other object that wouldn't otherwise be covered.
I agree with callen - a longsword by default won't be covered by Parma, but you can get round this by making it your talisman. I'd probably allow a Knife to be covered by Parma, and maybe a Dagger.
My experience with the School of Ramius is that it's not very good at taking things down quickly, as it doesn't do that much damage. This is probably why the example Ramian in Magi of Hermes uses a Poleaxe (+11 damage), although a Warhammer would be slightly better if you don't mind the extra weight. If you're only using a sword, that's at most +6 damage (+ Str + Attack Advantage), which is likely to be substantially less than the +15 damage from a Pilum of Fire. Unless you're using a ranged weapon (+8 damage for a long bow), you also need to close with your target.
You can increase those totals with enhanced weapons (and increase them a lot if you can get a decent trained group behind you, although that requires you to either weaken your own Parma or leave them unprotected), but the basic point still stands.
That suggests to me that good ways to deal with a Ramian include standing behind your shield grog and killing him before he can break through (bonus points if your shield grog can get some of his blood to use as an arcane connection, although with a Ramian's defenses that's likely to be tricky), flitting around outside his range and/or invisible and Perdo Corpus spells to inflict wounds directly, thus bypassing his soak. Setting a trained group on him is also good unless he's warded himself against mundane attacks.
Note that unless you're really good at Rego Terram, sponting Wizard's Parry is going to cost you a fatigue level per round, which isn't sustainable in a ongoing fight.
You cannot target what you cannot detect. The school also relies on Imaginem magics. When an invisible blade hits you, your magic resistance stops the magic affecting the species not the blade. Given how deadly not dodging is...
I'm pretty sure that a talisman counts as a magical object, even if it doesn't have any imbued effects, so opening a sword as a Talisman wouldn't make a whole lot of sense for a Ramian.
If swords, etc, aren't covered by Parma, it seems that every single Ramian would want to have Unravel the Fabric of Terram learned and mastered for fast-casting, along with a bunch of Finesse for high initiative rolls. That, or they'd need to carry a bunch of swords with them at all times so that it's no big deal if one of them gets destroyed or torn away.
This has been discussed a few times before, as the Rules aren't explicit on it (for example, at https://forum.atlas-games.com/t/magic-swords-penetration/7349/1). I think the correct view is that merely being a talisman doesn't inherently make something subject to magic resistance (although any active magical effects would), in the same way that just being a creature with Might doesn't mean you have to penetrate to claw someone. I've got a couple of reasons for thinking this:
There's no obvious way to give a talisman a penetration total - you're not generating a lab total, just investing an item with vis and then attuning it.
There are several examples of magi in the books who have talisman weapons - for example, the aforementioned Hugh of Flambeau in Magi of Hermes, and Phillipus Niger in Guardians of the Forest. Hugh of Flambeau does have a note saying that "Hugh has enchanted a long-hafted bearded axe as his talisman...Only the haft has been enchanted, allowing the blade to be unimpeded by magic resistance" which could be taken to imply that only the haft is his talisman, and not the blade, but I don't think compound devices work like that (especially as the component opened for enchantment is a tiny semi-precious stone), and he uses an attunement from the iron in the axe-head, so instead I think it's just referring to that fact that he's got an enchantment in the haft to make it hard to break.
That does assume that they expect to be fighting magi a lot. Back-up weapons are a good idea generally, though.