The smallest SHARP microwave DRAWS 1100 watts...or 91 AMPS (plus conversion losses....so lets call it 100) from your batteries during operation. If you have an inverter that can handle this, the damage to your battery bank is relatively minor 16 amps/hours for 10 minutes use. Microwaves typically do not like cheap inverters...get a sine wave or GOOD modified sine wave inverter if you want to run one off your batteries.
Hmm, I should go and check and see what I used on my trip, brb!
Ok, this is what I used.
Microwave is a Sunbeam SBM7700W
120 Volt A/C
So the microwave uses, what is that, 960 watts. I got that microwave at Walmart, it was on special for like 99$us at the time I bought it, or maybe it was 59$us, I remember it was something absurd and it was definitely under 100$us.
Inverter is a Vector MAXXSST w/ soft start technology (whatever that means!)
1500 Watt peak
750 Watt running
This may have come from Advance Auto Parts, I can't remember.
Here is a place selling one
I ran that off of 2 deep cycle marine batteries I got from Advance Auto.
Even though that cheap inverter (750 watt running, 1500 watt peak) doesn't say it's big enough to run that microwave (960 watts), I can assure you it ran it just fine, often.
I wasn't preparing like giant multi-course meals with the thing, of course, it was just me most of the time. The biggest meal I made in it was for me and this gardener at some Mexican RV camping place, and I think we had chunky soup, a can of corn, and I forget what else, just things you heat up for a few minutes.