Microwave will suck a lot of amps so don't go too small. I have a 2000 W inverter
and wouldn't go smaller.
Be aware that as a rough approximation, it will take ten times more amps at 12V from the battery
to the inverter than a 110V AC appliance uses. So a microwave typically pulls 10-12 amps which will pull over 100 amps out of your batteries
. Won't be for that long so the amp hours used won't be that great but you will need to size the cables battery
to inverter accordingly.
Also, microwaves will need true sine wave so you'll need to get a good (IE expensive) inverter. I have a Victron that has worked well for almost 10 years and love it. Mastervolt also makes good units.