Well... thanks a lot to Isaac for the help. We need some more info about the US but here's a bit of what I could find.
FAA uses some different types of aircraft (Beechcraft B300/350 still be the most common) for the navaids checks. As Isaac said, their callsign is FLC (Flight check) ## (where ## is the registration number of the aircraft) Ex, FLC79 for aircraft N79
I have found some B300s with registration N66 to N84 (that's a total of 19 B300s)https://www.flightradar24.com/data/aircraft/n70#94e5bed
Canadairs CL60 with registration N85 to N90 (that's a total of 6 CL60s)
I'll keep looking for some more. I'm sure some of those flights and ATC are so interesting. Imagine these operating in big airports...