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I don't think conductivity has anything to do with microwave absorption.
Try heating a pair of glasses, one with brine, the other deionized water.
I'll be surprised if the temps are more different than expected due to
variations in the microwave field with position
Take a look at the data
a) This thread started with a discussion of cell phones. At the frequency
of my cell phone (840 MHz), Jackson says there should be an
order-of-magnitude difference between plain water and sea water.
b) At the standard microwave oven frequency (2.45 GHz), Jackson reports no
data for sea water. I haven't tried sea water or DI water, but when I
compare New Jersey tap water with a saturated salt solution, the salt water
heats up more slowly, which is somewhat paradoxical. Perhaps it is so
conductive that it shields the inner part of the sample.