I splurged and bought a LiteVNA which is a Vector Network Analyzer similar to NanoVNA or SA2, but LiteVNA goes all the way to 6.3GHz so you can test and tune your 5.8GHz FPV antennas. NanoVNA and SA2 only go to 3GHz so for us, they generally are good for everything but 5.8GHz video.
This is a 2 port device so besides antennas it can do things like graphing the response of high/band/low pass filters. Because it is a VNA, it can measure the resistive/reactive part of loads. It can tell you "distance to fault" (open/short) in damaged coax cables. Lots more of course.
I bought it on eBay. You can get one for USD $117 (shipped, not including tax) with 2.8 inch screen from China in a month. You can get one for USD $133 (shipped, not including tax) with 4 inch screen from China in a month. You can get one for USD $150 (shipped, not including tax) with 4 inch screen inside USA in a week.
I've got something like 25 FPV antennas and some are completely worthless like the Eachine 6DBi patch (SWR of 3 to 15 across the band, but it is actually worse than that sounds) (it often comes with a metallic sticker completely covering the side with active elements, the SWR improves to 1.5 to 6 after removing the sticker and/or putting it on the back side). I've also got a lot of cheap antennas from eBay including some bad ones. Example: One 3 leaf was actually a 4 leaf with one leaf cut off (remaining leaves were not spread out to even them out) hidden inside a case. Example: One set appeared to be made correctly but was slightly and unevenly crushed when put inside a case that was a little too small.
You can get bad no-name antennas from many discount places. I don't feel bad about naming eBay this way because in my experience eBay doesn't seem to care if some of it's sellers sell stuff that functions poorly and does not meet the promised specs. They seem to be more interested in selling a lot of items than weeding out bad items. Yes it is easy to get your money back when it is not as described, and seller pays return shipping, but that is still a hassle. I buy a lot from eBay, but I have learned to fully test everything I buy. I bought this LiteVNA on eBay and am very happy with it.
On the good side of antennas, I have a great 8 turn Aomway helical and some great cheap 3 and 4 leaf (cloverleaf / skew planar wheel)... Now I know what is good / how good by just connecting the antenna to the LiteVNA and switching it on.
Of course this doesn't directly tell you the axial ratio or the smoothness of coverage. Those tests can be done but require separate transmitting and receiving antennas with a known good antenna and also preferably an automated moving test rig.
I've currently got my LiteVNA calibrated (it comes with calibration set) and set to display Smith and SWR charts from 5.6GHz to 6.1GHz. Of course it also works with lower frequencies like 433MHz (OpLink and LRS), 868/900MHz (FPV video and LRS), 1.3GHz (FPV video), 2.4GHz (FPV video and standard RC), etc.