I personally wouldn't tie Wild Magic into Miracles. The whole point of Miracles is that they work 100% of the time but you only get like two or three of them per scene, so if you start playing around with them mechanically it becomes exponentially more of a problem. But let's see- if you need a mechanic... Add in a dash of In Nomine: Failure = Spell goes off without issue. Success = Small, mostly cosmetic bonus. Threat/Crit = Caster's deity intervenes for their benefit. Error/Critical failure = Deity opposing caster intervenes for their benefit. Deities meddling is not necessarily good for the person asking for the miracle...
Yeah, a Resolve check is probably the best bet. It's the only mechanic I can think of that interlaces flat over nearly any part of the system without taking extra actions. Probably using similar mechanics but make it so the spell never fails. Roll a Resolve Check versus the Spellcasting DC of the spell and then either A: success = good effect, failure = bad effect or B: success = no effect, failure = cosmetic effect, error/crit = mechanical good or bad effect.
In the case of the particular campaign I'm intending to use it for, all the wild magic (both arcane and divine) is due to a meddling elder god of chaos, so that's not too far off, fluff-wise. But I did go with more or less Takeru's "B" setup -- but in this case, the critical failure produces a risky effect, rather than the same set of critfails arcane casters have, being a bit more lenient to the divine casters as a concession to the fact that divine magic is supposed to be more reliable.
Also, I figured out how to make fancy pretty PDFs like Big Jim does, so here's one of those
for my converted "Wilder Magic" campaign quality.