I needed to bore out some timing belt pulleys to a press-fit on a steel shaft. The proper tool for accurately measuring internal diameters is a bore gauge - these come in different kinds, but one popular variety is the telescoping gauge (see last two photos below). These have two spring-loaded plungers which are inserted into the bore then locked in place with a thumbscrew on the end of the tool. The distance between the ends of the plungers can then be measured with an external micrometer or calipers. Properly made and used, these are very accurate instruments.
However, I'd never used them, didn't have a set, it was a Friday, and I wanted to get the job finished (it was one of these jobs you wish you'd never started). I made a simple gauge to get the job done. It consists of two small 4mm diameter plungers which slide in a hole at the end of the main body. The body is split and a screw passes up to lock the plungers in position. The ends of the plungers are domed and polished by hand, since they must have a tip radius less than the diameter being measured.
It was a little tricky to use, but with a bit of finessing I managed to get it to work. To give specific numbers, I found that a 13.985mm bore in the aluminium pulley was a nice press-fit on the 14.000mm steel shaft (only 0.015mm of difference).