Magnets can also levitate over other magnets, so it's not only possible with superconductors. But it does happen with superconductors. The magnet will induce a current in the superconductor, which creates a magnetic field, which repels the magnet.
Earnshaw's theorem describes why a free-floating (paramagnetic) magnet cannot levitate over another such magnet. There must be at least one stable axis which is not from a magnet. See https://en.wikipedia.org/wiki/Earnshaw%27s_theorem
> The magnet will induce a current in the superconductor
That's a different sort of levitation. See https://en.wikipedia.org/wiki/Electrodynamic_suspension . We know it's not the same because you can see a magnet floating above a superconductor even though there's no motion.
The relevant reason is https://en.wikipedia.org/wiki/Superdiamagnetism .
] Superconducting magnetic levitation is due to superdiamagnetism, which repels a permanent magnet which approaches the superconductor, and flux pinning, which prevents the magnet floating away.
] Superdiamagnetism is a feature of superconductivity.
> In both of these magnetic repulsion videos, keep in mind that magnetic repulsion and/or levitation are not, by themselves, probative of superconductivity: a diamagnetic material such as pyrolytic graphite [16], can be made to levitate [19] in a magnetic field without being superconductive.
See https://en.wikipedia.org/wiki/Magnetic_levitation#Diamagneti... .