I used a 700 watt microwave & a 5 cup 600 watt drip coffee maker with a 1500 watt PSW inverter on a pair of 232 amp hour 6V golf cart batteries, recharging with between 360 & 420 watts of solar. There were days that because of clouds, rain, etc that I skipped the microwave use, but almost always made the pot of coffee. Used 6-8 amp hours for the coffee. As long as you monitor the batteries & have a means to recharge them, it will probably work. Some microwaves are pretty inefficient, which could present a problem.
That said, when the microwave died, I replaced it with a 950 watt Panasonic inverter microwave. The advantage of the inverter type microwave is when you dial down the power it actually drops the input wattage. At lower power levels, a standard microwave runs off & on at full power. When the batteries are low, I can dial down the microwave to as little as 300 watts. It also does a much nicer job of defrosting - no cooked edges of food.