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). Therefore 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.