I just saved this info from somebody very knowledgeable, Lou Schneider on the Escapee Forum. (we intend to follow his advice)
" I use my microwave on my inverter all the time. I have a Dometic 1250 watt microwave and a Whistler 1500
watt modified sine wave inverter that I bought at a truckstop. With a modified sine wave inverter, the power drawn by the microwave will decrease and the cooking time will increase compared to using true sine wave power. If the microwave worked at 100% power on the inverter, it would draw about 100 amps from the batteries, but in actual use it's draw is more like 70 amps and the cooking time increases by about 50% compared to using it on sine wave power, but other than that the microwave works fine.
The thing to remember is you're only drawing that power for a short period of time.
70 amps * 10 minutes of use to warm frozen leftovers or cook a TV dinner is about 12 amp-hours. I have two golf cart batteries so that's 1/20th of my rated capacity, or 1/10th of the usable storage. You don't want to draw the batteries down more than 50% of their rating for best battery life.
Make sure your inverter's primary cables and connections are large enough to handle that amount of current."