What happens when you place it below a magnet? It becomes pinned, upside-down.
If you place it on a magnetic track, the superconductor will follow the track when an external force is applied, and continue to follow it until it loses its superconductivity (due to temperature) or until air resistance slows it down. This works upside down too. The disc in the video below can lift objects 70,000 times it's own weight which means that this particular disc could lift a small car.
This phenomenon is known as quantum locking. A property of type-II superconductors is that they try to rid themselves of magnetic fields, but they can allow concentrated flux lines to pass through at certain points which are proportional to the material and the area. This effectively pins the superconductor and allows it to levitate.
Boaz Almog gives an excellent TED talk on the subject. Check it out here