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The [portable microwave] appears to have rather limited power when not connected to either the battery directly, via the jumper cables, or to AC. I've seen similar reports of it being underpowered, but it seems in all cases they were using the cigarette lighter cord.
Well, that's not surprising. A typical cigarette lighter socket on a boat will supply at most 5 amps. Any more than that and the in-line fuse or breaker blows. The power available to the microwave is therefore 5 amps x 12 volts = only 60 Watts max, and the microwave isn't 100% efficient at converting that input power into R/F. The portable unit on the cigarette lighter would take around 20 times as long to heat something as your typical built-in 1000 Watt house microwave.

Hmmm ... 1 minute to heat a cup of water at home, 20 minutes to heat a cup of water in the portable unit. My stove is faster than that! I wonder what this portable microwave draws when connected directly to the batteries?

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