Well flip me sideways, an off-the-wall theory turned out to be basically right for once.
Those U.S. diplomats in Havana and Guangzhou suffering the mysterious, hard-to-pinpoint neurological issues? Turns out
our doctors now think it really was a microwave attack, using something called the Frey effect.
The original goal, for use in your atompunk games, was either mind control (by inducing delusions that spurred desired behavior) or long-term subtle physical damage (by inducing slow injury to the nervous system). Communication is also a possibility (the beam can be very tightly focused, and needs no discoverable receptor other than the human body), but the side effects might be a bit too much for any but the most occasional usage.
Note that these effects are separate from the painful, skin-deep effect employed by Microwave Area Denial systems, which simply induce a burning sensation.