The exclusion of magnetic field lines from a superconductor is called the Meissner effect and a strong magnet will levitate above materials in their superconducting state.
A small strong magnet is sitting on a sample of YBa2Cu3O7-x. Liquid nitrogen is added and the YBa2Cu3O7-x cools and changes into its superconducting state, resulting in levitation of the magnet. A small strong magnet levitating above a superconducting sample can be spun. No matter what the orientation of the magnetic field, the field lines are still repelled by the superconductor. While it is possible to levitate one magnet using another magnet, it is not possible to maintain levitation between magnets when one of them is spinning. When the superconductor warms above its critical temperature, the magnet field is no longer repelled and gravity wins. Levitation of a large magnet by a superconductor.