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.
I don't think that works as advertised: Any measurement of the current will likely produce a magnetic field itself -- for example from the current in a Hall probe. This current will induct a small, opposite current into the superconducting coil. So the current will go down.
And even if not, what you would need is to measure the change of the field over time. This has finite resolution, so you can't distinguish no resistance from very very small resistance.
There are several tests that have been ongoing over decades doing exactly this. The small loss of current during measurement occurs, but you only engage with the field intermittently, and you can calculate approximately what the loss should be.
Yes it could be some tiny resistance, but the same issue occurs with the resolution/accuracy of the voltage or current measurement you would make.
Exactly my point. You cannot measure that the resistance is exactly zero, you can "only" give an upper bound. The upper bound depends on your approach, but no approach can give you a zero upper bound.
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.
