Getting rid of public communications infrastructure would be quite easy. Just use your might to get rid of the ISPs and force the telcos to only use landline phones and, other than the phones, you basically don't have any modern communications systems your average joe can use anymore. Well, other than CB radio, that started in 1945, but anyway...
The challenge would be in removing HAM and CB radio operators with modern equipment. I don't think you can actually do that. I don't know of anyway you can detect the type of equipment somebody is transmitting with, other then that tube amplifiers and solid state amps have different overdrive/clipping characteristics, but I don't know if that would ever really be detectable during normal operations.
Actually, reading your question again, it seems like you didn't consider that there are people who privately own transmitters and communicate with each other with them, and did so even in the mid 20th, or even late 19th century.
For a scattered resistance, using mid 20th century radio tech would be just fine. The biggest changes in modern communications technology have been bandwidth and carrying capacity and for coordinating a resistance you don't need much of either of these things.
There really is no effective way to prevent electronic communications though. The bar to entry of radio is really just money. There's no special factory or manufacturing technique you need, just give your average Electrical Engineering grad $5000 and they can make you a high power transmitter from off the shelf components.
It would be easy to find somebody who was transmitting (though their might be some stenographic techniques you could use to hide in background noise or authorized communications), but if they need to send one or two messages, that might be enough and with cryptography you wouldn't even know what they were saying.