I have a 2000i Honda... We used it to power our deer shack which was a 37 ft 5th wheel camper. We would run pizza over, playstion, TV, all the lights, fan ect on the 2000i. The generator would bog down when we started the microwave or the pizza over but always powered it fine even with all the lights, tv, playstaion, fan ect all on at the same time.
I would think that a 1000i would power a small microwave just fine if that is all you will power other than maybe 1 light, but thats still just a guess. Honda generators are AWESOME! They sip gas, start easy even in the cold, are quiet, smooth, ect.......
Gander mt has good prices on them most of the time.