If all you are dealing with is professional LMR radio, that simplifies things greatly. Most all of it can be readily identified on sight by nomenclature. Post some pics and whip lengths, and let us take a shot at it. Sounds like a fun exercise. Then you can tell us how accurate we were after you test them.
As for the machine, a test monitor and/or an SWR meter should do the trick. Transmit through the antenna in the four different bands until you find the band with the lowest SWR, and there ya go. Then you can fine tune to find the actual resonant frequency of that particular antenna for a more precise determination. For example, finding out that it is UHF is the easy part. But determining whether it is cut for the federal band (401-420ish), the LMR band (450-470ish), or the UHF-T band (482-512ish) will take a little more time and testing. Definitely doable though, without much hassle or expensive equipment. Good luck!