It's a limitation of the most basic approach to the problem (measuring resistance), but not a limitation of every approach (such as measuring current).

You can inject a current into a superconducting coil and take measurements of the resultant magnetic field as the current circles for an indefinite period of time. I'm not able to see how this approach analogizes to water in a cup.

Would one method (assuming a pure sample) be to pass a high current through it and measure if it heats up? I know nothing about this, but that would be my first guess.