I have seen thread plates that you can screw the offending fastener into to find the size but only in metric and sae – there may have been a whitworth one as well i can remember .
I know little machine shop in the USA do have one part #3459 but shipping will cost you .( usual disclaimer applies )
I use a similar method to Les which only works if you have a nut that fits the screw you want to check .
I use a peice of scrap as a holder so it leaves my hands free to operate a height gauge to measure the diffence in height the screw moves after 1 turn of the nut .
Bascally i measure the screw dia then find a drill a little larger than this but as close to the screw dia as i can get .
Then drill a hole in the scrap and set it up in the vice of my mill on some parrallels and get a height measurement with a height gauge , i screw 1 turn and re measure .
The difference is distance travelled per turn .
Divide 1inch by this and see what comes up if it looks odd then convert to metric to see if there is a match.
Sounds long winded but is useful for small screws and only takes a few moments to do but if you have some scrap flat bar large enough to sit the height gauge on then the set up for the milling vice is not needed as it can be clamped in the bench vice .
I have found the thread gauges that you get with a tap and die set are useless for anything with a fine thread and the fine metric units hard to see for small screws .
Ian