@kravietz Aircraft are extremely resistant to EMP as they get struck by lightning all the time. Plasma has weird properties and it's rather strong.
The hardware controlling the drones can be swapped to radiation resistant hardware in addition to shielding materials inside or outside the drone.
The weapon has to have a cool down period between firing and another swarm could come in during that time.
A really cool technology is being brought back for fast flying small targets and it's the shotgun. There have been experiments in the past to extend the lethal range and effective range. I believe that one used buckshot and was effective to around 200m. The fastest way is likely going to be a thermobarric volley so it will crush and rip them apart or just damage the rotors.
Thermobarric rounds are really cool and should work decently, they work better when there are chambers or something to help with the pressure wave. It should still work well and not have much falling debris.
The truth is that it could be a threat made from regular quadcopters to something much more rugged. The weapons will have to evolve along with the drones.
From what I've seen being used, a shotgun could work or use those 40mm under barrel launchers to get an easy 25m kill radius. The only modifications needed would be an altimeter and an inexpensive optical sensor paired with a processor. (Honestly it could be an inexpensive smartphone) The rounds could use time and atmospheric pressure from the ground unit to detonate. So that's a soldier operated unit which are seemingly the same on the AK and M16/M4.
Just found this Skynex demo, which deals with a swarm quite effectively. Looks like shrapnel or buckshot (?)