You can easily measure to 0.1 mm using ordinary micrometers and such. A depth micrometer from a a flat of know thickness will give that precision for height If you need higher precision, say 0.02 mm, then get a surface plate and height standards. You compare the height of the rim or base to the standards using dial caliper on a stand or similar electronic caliper.
When you mentioned using a web camera, it gave the impression that you did not need great precision. Have you ever done such measurements of an irregular or round 3D object with a web cam? There can be a lot of distortion.
John