Microwaves (or more accurately microwave ovens) are something of a luxury when living in a vehicle! They are pretty rare in the nomad world, more commonly found in large vehicles because they do take up a decent amount of space and have high power demands. Nomads who spend a lot of time connected to shore power or who have very large solar power systems may find them worthwhile.
Microwaves can draw significant phantom power loads, so you may wish to unplug them when not in use, or get a model with mechanical timers and power settings.[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 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% more inverter rating than cooking power to operate.[2] For example, a "700w" microwave requires a ~1000w inverter, Pure Sine Wave preferred.
