As we know, superconductors have zero resistance. How can we measure the zero resistance in a superconductor? Can you devise an experiment to measure the zero value of resistance?
You can take a superconducting magnet and set it up to run in persistent mode. Here, you have a current running around and around in a loop of superconductor with no external source. If the current indeed persists (based on weak measurements of the magnetic field), then the resistance must be zero (or at least quite low, depending on the uncertainty).
As the other answer point out, you can devise simple methods that show the resistance of a superconductor is zero within the limits of experimental error. The size of your experimental error will depend on the precision of your measuring instruments and the length of time over which you conduct your experiment. This Wikipedia article says
... currents injected in superconducting coils have persisted for more than 25 years (as of August 4, 2020) in superconducting gravimeters.
Note that often, superconductivity is established not by directly measuring resistance, but by the Meissner Effect: "the expulsion of a magnetic field from a superconductor during its transition to the superconducting state when it is cooled below the critical temperature. This expulsion will repel a nearby magnet."