Andrew,
This is my interpretation. I would take the objective end of the scope and measure with a caliper. Take that number and divide by two. This will yield a number from the center line of the scope to the bottom of the objective. The next step gets a little more complicated. I believe if you are using picatinny type base, ring height is measure from the top of the picatinny base to the center line of the ring (Seekins precision has a good diagram). As far as getting a height of the picatinny rail, I believe you would probably have to contact the manufacturer or install it on the gun and measure. Barrel contour/taper will probably play a huge factor is mount selection. You should be able to do some math and determine which ring height will work for your application. As for standard type ring/base combination (ie Leupold) I believe that the ring height is measured the same way, but I do not know about the base height. Anyway, just my take on the matter, I may be dead wrong. Hope this helps. Just a personal note, on most of the leupold dual dovetail mounts, I have been able to use one size shorter ring than is recommended on the leupold website.
Chris