I do not like the term "levitation" as it is misleading. I prefer something on the lines of "suspension".
When in the presence of a magnet a superconductor is neither repelled nor attracted to it. For the sake of this discussion, we can neglect type I and II superconductors. What actually happens is that the magnetic flux exclusion makes it such that the magnetic field lines wrap around the superconductor.
This wikipedia link shows a sketch of the magnetic field exclusion.
In this configuration the superconductor will not move up or down (of course if you apply enough force it will). It is trapped in its position. If you put the magnet on the bottom it looks like the superconductor is levitating. Conversely, if you put the magnet on top and pull it up, the superconductor will follow it so that its relative position does not change (again, it is trapped withing those magnetic field lines).
But beware, if the superconductor is heavy enough it will fall and you will like shatter your ceramic :-). Done that :-(.