There is a clear maximum for Abilities based on character age, but is there a similar maximum for Arts?
The only limit on your Arts is the availability of XP to increase them with (and, implicitly, the availability of texts or vis to study to gain those XP).
There is the recommendation that
A sensible maximum for a magus’ Arts is 10 plus one for every four years since apprenticeship. Thus, a magus who is 20 years out of apprenticeship could have a highest Art of 15, while a magus 120 years out of apprenticeship might have a highest Art of 40. (Ars Magica 5th edition, p.32)
but this is not presented as a hard rule, only a "sensible" suggestion.
Also, note that the age-based cap on Ability scores applies only at character creation:
Your character’s age determines the maximum score she can have in any Ability at character creation. These limits do not apply to characters in play, and there is no cap on Abilities during play. (Ars Magica 5th edition, p.31)
If you use the optional "Extremely Complex Character Generation" from the sidebar on p.33, the Ability limits do not apply even then.