I used a 1000w PSW inverter as "whole house" when the MW was a smaller "700w" one. It wanted 1050w input. The inverter ran it ok, but showed an overload light for the time doing that (only a few minutes of MW at a time of course--normal MW operating scenario.)
It ran the kettle or toaster no problem at 900w approx. for the short time each that took. (Resistive loads)
Eventually, the inverter fried itself running the MW. It seemed to have been an accumulative thing, where I "got away with it" a few times, then didn't.
It is better to have a bigger inverter and not run it so close to max so often for it to last longer. Same with anything really.