You would use metals as your leads and create Josephson-junctions-like interfaces.
Basically the abrupt change in electron mobility across materials can cause knock on effects that dominate what you are trying to measure.
Interfacial engineering is one term in materials science that implements best practices for dealing with such challenges.
Perhaps heating it up while it levitates would be a better idea. Put the magnet in an oven together with the sample and bake?
And it's ridiculous that I'm saying that on the context of testing a superconductor. But well, here we are.
I do expect people to fully characterize it eventually.
Neo magnet fabrication is fascinating by the way, the somewhat magnetized blanks are not all that impressive from a magnetic field strength point of view, but then you zap them with a strong enough field and they then suddenly are the best thing since sliced bread.
This technique was first developed for 'regular' ceramic magnets.
https://idealmagnetsolutions.com/knowledge-base/how-neodymiu...
An uncoated magnet will oxidize very fast, so you always have to ensure that the coating on any magnets you use is perfect or the magnet will surely fail.
This gives a low resistance and diamagnetism which is used as proxy to real superconductivity.
I may be wrong though.
So many questions. I assume this is all possible but they are focussing on one thing at a time to duplicate the results, if possible.