Microwave ovens can be useful where shore power is available or in warmer climates where you don't want extra heat. However they draw a lot of power when operating, and can draw significant phantom power loads. For camper use models with mechanical timers and power settings may be more appropriate.1)
The benefit to microwaves is that while they draw a lot of power, it's typically only for a short period of time (rarely do people need to run a microwave for more than 5 minutes, while stoves or ovens might draw that power for hours and hours at a time). Therefor it is possible to power a microwave off grid without overbuilding the electrical system.
Smaller microwaves typically draw 700-1000w and larger residential models are commonly 1500w. As such you will need a fairly large inverter, but might not need too outrageous of a battery if you're only using it for a few minutes per day. See How much power do I need? for estimations.
Microwave power ratings (“700w”) are cooking power, not the amount of power the microwave will consume to operate. It will take ~50%2) more inverter rating than cooking power to operate. Example: a “700w” MW requires a ~1000w inverter, PSW preferred.