If the capacitor passes these tests, we put it in the oven for an hour at about 60°C and test again. This is because the insulation properties do deteriorate as the temperature goes up.
The mica condensers, although up to a hundred years old, more often than not test out OK. If they need to be replaced, it is usually because of physical damage rather than a loss of electrical performance.
As for the paper condensers, well to be honest we used to get so many failures when testing that we don’t even bother now – we always replace them with new ones. Even NOS ones fail.
CAUTION: Sometimes vintage test equipment becomes available but be careful. We have a combined coil and condenser tester which, when we used it to 'test' a condenser, it passed even though we had already rejected it. Further examination showed that the test meter only used 60v to test the insulation........ The tester makes a very nice looking ornament and a good conversation piece but it's not much use for anything else!