You could not use a conventional focused microwave beam because you'd need a very large antenna dish to do that. Granted, you could imagine a nanotech dish deploying very quickly when shooting - sort of a large umbrella opening. But that's unwieldy.
You would need very advanced metamaterial technology to build a linear, room-temperature MASER amplifier in the shape of a barrel. Once you have that, you also need very efficient transducers and very powerful supercapacitors (you can do with current technology but you need a handle like a battery drill and God's own heat exchangers, or large parts of the device would melt or catch fire).
Finally you're left with Flash Gordon's ray gun: a pencil-thick MASER beam that will cook anything in its path, unless protected by a conductive shielding. Given that there'll be Joule energy transfer, the shielding can't be just aluminum foil, you need something like copper (or even better, silver) mesh chain mail.
In practical terms it's not very much better than a bullet gun, and in several ways, it's worse, except perhaps somewhere you can't risk perforation damages or splinter ricocheting:
- the weapon is line-of-sight, very much like a bullet gun.
- no traces are left except on the victim - no powder smears, gases, spent cases or anything - and the noise is probably reduced. Unless the MASER bolt triggers some kind of sonic boom, not unlike the thunder from a lightning discharge.
- it can only shoot a few shots before you need a fresh battery (magazine).
- the range is limited. Not affected by wind and droop; but fog, rain and heat haze might be an issue.
- shielding is much easier than against a solid bullet
On the other hand, time to target is negligible, so you could have some kind of friend-or-foe autotargeting system and actually make it work.
Also, shape recognition could allow "impossible" shots - just wave the gun in the general direction of the target, and, provided it ever gets aligned, even for a millisecond, the gun could successfully shoot the victim through an eye. Defensive shields could feature wide-spectrum face simulations to thwart this approach, though.