Jamming would address inter-swarm communications, but then they'd revert to solo operations. EMP isn't realistic, but microwave systems have already been tested:
Birds and insects are able to swarm without telepathy, and the dynamics of this are fairly well understood. I don't think this is going to be such a big issue for drones; if anything, you'll get swarms of ultra-cheap tiny drones whose job is to swoop around chirping to each other until they get jammed, then take note of where the jamming signal seems to originate, GTFO, and convey that geographical information back to base at the earliest opportunity. The more enthusiastically you jam, the sooner you become the target of a ballistic mortar or guided missile that's fatally attracted to your jamming device.
Jamming wouldn't break line-of-sight or optical communication. Imagine drones that can simply see one another, and communicate by changing color (e.g. with LEDs).
Lasers are already used for inter-satellite communications, so there's no need to just use gross color shifting (though perhaps the BOM impact would be less).
Related side story: my resume had something about PKI in it so I kept getting calls from Boeing recruiters trying to fit me into a job doing said satellite laser comms (presumably using PKI). I kept telling them I knew nothing optics-related aside from basic Newtonian stuff, and they kept calling me back. I hope they finally found someone.