A permanent magnet begins to hover above a ceramic material as it cools and transitions to a superconducting state; the magnet remains aloft until the ceramic warms above a critical temperature.
The ceramic material is a 25mm disc of yttrium barium copper oxide (YBa2Cu3O7, also commonly referred to as "YBCO”). The YBCO has a critical temperature of 90K and is cooled with liquid nitrogen, which boils at 77K. The magnet is just under 5mm per side and weighs about 0.8 grams.
The magnet is able to levitate due to its interaction with persistent electric currents that expel external magnetic field from the interior of the superconducting YBCO. (The details of this interaction are complicated, and cannot be fully explained using classical physics.)
For more details on our setup and references for further study, see http://sciencedemonstrations.fas.harvard.edu/presentations/meissner-effect
Also check out this video from the Annenberg Foundation on high-temperature superconductor research http://www.learner.org/courses/physics/video/vid_byunit.html?unit=6&vidNum=1