Would you allow someone with the noncombatant flaw to engage in certamen?
Specifically, the noncombatant flaw gained from the second ordeal of the Criamon path of walking backwards - you are a healer, so you don't fight! I'd be tempted to say yes, since really, certamen is just a non-damaging form of magical arm-wrestling... but I am quite open to different opinions.
No. It's a duel.
I would leave this to the individual character to determine. I say this because, in my game, I've got two characters with the Compassionate Flaw, and they refuse to engage in Certament, considering it too violent. This seems completely unsupported to me, but hey, I'm not here to tell players how to play their characters.
If a magus with noncombatant thinks his attitude extends to Certamen, then it does. That's what I'd do.
I don't think it has to apply, but on the other claw, some people consider video games too violent, which is about where I would put certamen in terms of the violence scale (to be fair, it is possible to get hurt through certamen, but generally not much and it isn't likely... maybe more like a foam sword fight?
Hmm. So is a duel of wits.
Note that technically certamen only means "competition", i.e. duel without the martial connotation.
Both mages sit in front of each other and in the end, one is more tired then the other. For me non-combatant is about hating violence and certamen is not per se violent. It can be everything the mage wants it to be.
So i would let your players decide for themselves and not "trigger" the flaw if they decide to use certamen