What trade should I hire to vent a microwave through my roof?
Some microwaves come with an optional "vent to exterior" feature. We require a vent when installed over cooktop or oven. It comes with a charcoal filter that recirculates the air, but a small steel "flap" can be removed in the back and hooked up to duckwork and extended to exterior...it doesn't need to go through roof...whichever is easiest. Make sure it has a "backdraft" flap. 

I'd use a carpenter/handyman. Get a bid, make sure their licensed and ask for references.