You don't mention what size your microwave gross watt rating is, but my 2000w PSW inverter struggled to run our 1500 watt (gross) microwave...This was the same size oven we had in our stick house!! I switched it out for a Panasonic 800w unit (about 1100w gross) and problem solved...MW ovens are cheap, enjoy your inverter...
A BIG P.S.... I just noticed your previous 13 page thread, and I can say this from actual experience:
Though some of the responses suggest otherwise, Two batteries in good shape will/should run your MW without a hitch...I use our MW regularly from two 6v batts...Whats more important is that the oven is 'sized right' for your particular application (considering inverter ratings, inefficiencies, M/W size, and the normal electrical bottlenecks), and that the battery cable size to inverter is more than adequate - in this important regard BIGGER is waaaay better otherwise you'll experience low voltage alarms (announcing a voltage drop bottleneck) on the inverter...
Another thing is to check the 'surge rating' (if published...) of your inverter...For instance, motors and (to a lesser extent) M/W ovens have an initial/start surge requirement that is often much higher (say for a few milliseconds) than that of their 'nominal' power ratings, likewise a quality inverter will have a surge rating say about 25% (or even more...) of it's nominal (advertised) watt rating, so to safely handle these very brief start-up surge loads...A rule of thumb is the higher the cost of the inverter, the better are the electronics, thus a higher 'published' surge rating.
3 tons