Three quick points:
1) The rating on your microwave is output power. Since the unit is not 100% efficient, it has a greater input power than output power. (See the note above about driving into the desert).
2) I have a 650watt microwave on my boat. It fully "loads up" a ProWatt 1000 inverter. I have size 2 cables feeding the inverter, and it is less than three feet from the battery bank. Loss of voltage at the inverter input will significantly degrade its ability to make rated output.
3) Your battery bank capacity has to be great enough to provide a high level of DC current to the inverter, without the supply voltage dropping off. I have two banks of two Group 24 batteries, and use all four in parallel (ALL on the battery selector switch) when using the microwave.
2002 GW Islander 270 - 2001 Yam 250 OX66. Fishin' & cruisin'