An explanation as to why an UPS manufacturer may caution against using inductive loads.
While the question is about microwave ovens and is it inductive, or will it work with your UPS, i think this answer will help you understand the manufacture's caution. Many UPS do not generate pure sinewaves. Many electric motors don't perform as well with anything other than sinewave, drawing in more current that can lead to over heating and shorten the life of the motor.
Inverters can be generally classified by their wave forms. Examples may include sine wave, square wave, modified square wave, modified sine wave.
For the purpose of differentiating types may be define as: (Note) Maybe not everyone will agree with these conventions, but they are in use and i welcome any suggestions for improvement on this answer.
- Sine wave: pure sinewave or pwm sinewave: Outputs something very close to a pure sinewave. Usually pulse with modulated square waves at relatively high freqency with varying duty cycles and smoothed with an inductor and capacitor to very closely approximate a sine wave. See figure 1
- Square wave: outputs the same rms as a sine wave but at a lower peek voltage than the peek voltage of a sine wave, the square wave tha5 steps from + to - voltage at 100% duty cycle. See figure 2
- Modified square wave: typically output a square wave that steps between +,0, - voltages with a duty cycle less than 100% and a voltage peak higher than that of square wave inverter. See figure 2
- Modified sine wave: output square waves at several voltage steps so as to roughly approximate a sine wave. See figure 3
You might want to look into what kind of wave form your UPS generates.
Aside from motors, you may want to look into what does or does not do well with your inverters wave form.It may or maynot effect your devices. There is a lot of debate on the topic with some of it being more or less informed.
Lastly, in general microwave ovens tend to perform optimally with sine wave and Ok with modified sine wave. There may be issues square and modified square wave.