Why won’t my Champion C46540 generator run the microwave?

That model is rated for 3.5 KW continuous, and has an automatic voltage regulator circuit - so it should be capable of powering just about any microwave oven.

Microwaves aren't particularly picky about the AC line frequency, so it should still work even if the frequency is a few Hz off.

You might try measuring the AC voltage at the same receptacle the microwave is plugged in to - while the microwave is running. Look for excessive voltage drop as soon as the microwave is turned on.