Sounds so expensive, heavy and like a chore.
A solar array, battery bank and inverter is a much more suitable setup for this situation. Microwaves don't need generators at all. They pull a lot of current but only for 10-15 minutes here and there, so Amp HOURS used is actually small.
Solar keeps the batteries topped off at all times too, unlike generator only setups. It's silent, always on and working and handles a situation like this with ease and no need for fuel.
These is no better case for solar than this one.