I have a group of players who want to be able to keep their mages through into Modern day. We are playing through a "Transforming Mythic Europe" scenario where the Order comes out to Mundanes to form the 4th Estate.
What would need to happen for mages to be able to survive into the modern day?
Well, in principle a Breakthrough allowing the creation of longevity rituals that don't cause Warping. But, I'd suggest doing the opposite: instigating a political change in the Order that will allow it to accept members with Might, i.e. immortal wizards. And concurrently a introduce way or ways to achieve said immortality, so that the standard trajectory for magi would be to become some sort of Immortal magus.
This has the advantage that growth through Experience is effectively capped; otherwise, you'll get some crazily-over-experienced magi around. And I think it's more colorful. It would be a pretty massive change to the current system, however.
Concurrently with it, I'd advise a plotline of "Diminishing Magic" where the number of Gifted children drops, so as to keep the total number of magi manageable.
One option to do it is just to allow a Breakthrough that allows magi to become a Magic Being upon entering Final Twilight. Perhaps discovered by a Criamon or Bonisagus magus, and spread throughout the Order. This is the simplest way.
I'd actually prefer to have a variety of Immortal types, by having multiple ways of becoming immortal spread throughout the Order. Some through House Cults, others through Order-wide Mystery Cults. Some examples:
As a minor change to House Bjornaer, allow their Great Beasts to be their Inner Heartbeasts, but with a Fast Acclimation flaw so that they tend to stay in the Magic Realm.
House Criamon already has a variety of ways of becoming Immortal. Utilize them, especially the Tangential Magi.
House Merinita already has immortal magi through (Faerie) Becoming; let them be known.
Let Hermetic Alchemy spread through House Verditius, and perhaps beyond. I'd perhaps amend it to transform the magus into a magic item rather than purified flesh and blood.
Let House Tremere develop a House Mystery Cult revolving around spirit-magic, including the Living Ghost.
Let the Tytalos Titanoi become servants of the Titans, a la Votaries.
Let these, or similar, Mystery Cults generally spread throughout the Order. So you could have the Order of the Green Cockerel (perhaps separately from House Vertidius) allowing magi to reach alchemical immortality, a large surge in the Titanoi as more and more magi become subservient to the old Titans, an astrological cult which teaches worship of the stars and apotheosis as a new star (Ascendancy to become a Daimon), and so on.
That's a lot more work, but more interesting, IMO.
Finally, consider what Science is in your setting. You could decide to do a Magical Revolution instead of a Scientific one; I'd do that, personally, as combining magic with science leads to one big conceptual mess, and as a lot of technology could be implemented magically rather than through science. If you do do that, consider whether you even NEED to reach modern times. The "Magical Revolution" could develop quickly, so that you'd reach current-levels of magic-tech within the magi's standard lifetimes. Do you really NEED to go to the 21st century? Wouldn't just reaching the 15th century, after a fully-developed Magical Revolution, suffice?
Instead of the Age of Reason and the ever encroaching dominion stiffling all magic the Age of Magic comes fully into capability. No need for science when you got magic, 'You say you can build a machine that runs on steam? ...why would you bother when we got magic propelled trains??? Thats it your insolent ideas have no usefull purpose here at the university, here we teach usefull stuff, like how to boil water with your mind!'
If the dominion and reason can be held at bay, the old beasts not be slayed and magic resources in general not harvested to extinction, then nothing should keep magic from entering "modern" day, but it wouldnt be modern day as we know it
But what breakthroughs could not be achived in this timeframe? What wonders built? What wars waged? An end with a atomi... magic winter covering the lands for a thousand years is far more likely, given humans capacity for wanting more.
I can foresee two big ones: one against the Dominion, because magical beasts, vis sources and magical auras are already ("already" meaning XIII century) starting to shrink. That war would be epic by itself, because fighting the forces of God have a lot of moral background enough to flood any saga, but unavoidable unless you want magic to fade out from the world.
But the second war I can imagine would be even worse: I just thought of a world were magi can become immortal, so a world having a cluster of pretty much almighty beings around. Such magi would finally become a force of such power that probably would dominate the world. And then what would the French Revolution be? Mundanes raising against that world oppressors, which happens to be the Order of Hermes?
However, two things can happen concurently: as magic users (regardless of the tradition) are doing their coming out, magic will become more prevalent, especially lesser magical items or charge items. But power to manufacture these items will still remains within the hands of very few people.
So instead of slowing the Scientific Revolution, it might have the opposite: people will seek in science what they cannot have because they don't have the gift. And in fact magic could greatly help the advance of science by providing analical and scientific tools that are hard to build.
Finally, the most advance society will be the one managing to combine the use of both. More technological machine require a form of energy: heat for the most basic one, then steam and finally electricity. However, the bottleneck has always been sourcing or generation of said energy. But with a little bit of magic, you can break these constraints. A small CrIg lesser enchantment can provide all the heat you need, combine with the creation of water (not permanent), you generate endless steam. So steam trains becomes very easy to supply and any steam powered machine won't have to deal with truckloads of coals and cistern of water. But before this ideal combination of magic and science, I am sure they will be great rivalry and underground plotting for those trying to get more power.
On the other hand, I am not sure mages with see science and scientists as rivals: after all, if they succeed, mages will have less spotlight and be able to return to their favorite activity: quietly studying in their labs without having to answer pesking requests about a drought, a flood and whatever inconsequential issues that plagues mundanes .
Regarding the power curve of very old mages, you need to find a way to address it. By definition an immortal mage, not constraints by Twilight or by the immutability of immortality will be able to do whatever he wants. So the chapter in Mysteries (p133 Immortal Magi) gives a very nice frame to keep things more or less under control - at least slowdown significantly the powercreep.
Not that powercreep is not bad per see, but it will change the type of stories you tell. With more or less unlimited powers, mundane issues becomes irrelevant and only world changing story are worth investigating. Also, if the players PC are very old, unless they manage to have a very unique way to achieve that, there will be many other older mages. What do such powerful being on a daily basis ? What does such a community ? If they are stuck in their existing passion/interest, does it means that lasting feud will never die (like Verditius Vendeta) unless the Immortal being decide to change permanently his nature through an enchantment ? Does it leads to pointless and endless fight, with plans of revenge spanning decades or more ?
Does an immortal mage passionate by bees will keep studying only bees, thus become the ultimate references in bees, de facto a Bee-God ? Is it going to lead to the birth of new gods or at least patrons ? After all, their mortal life would pale in comparison to the duration of their total existence.
I would be very interested in what the modern day would look like in Ars Magica, like you can’t exactly have Apollo 11 or any missions to the moon (unless God is welcoming to visitors in your saga) as well as what modern medicine would be like in a world where the humor theory is true, as well as what the Americas would be like. Would the native Americans be able to prevent european encroachment? How would computers work under the metaphysics of Ars Magica?