How do you measure the most accurate measurement devices?

Or more simply, if I have access to a device that measures something with a certain, known accuracy, and I have a device with an unknown accuracy that I expect to approach that of my known device, what sort of math should I be doing statistically? How is this generally handled in science/engineering?

Edit: there's been one cool answer which is measuring something different that you correlate using scientific theories. However, that doesn't really explain my original (intended) question of what you do when you're measuring the SAME property directly.