Quoting a comment in the video linked to by fybren:
"This levitation is NOT due to the Meissner effect. It is negligible since we use thin films. If it were the Meissner effect the field would get distorted on a length scale of the diameter (~cm) and then two discs hovering above and below each other would affect it other. Which is clearly not the case. The discs are actually trapped in constant field contours rather than levitating."
"This levitation is NOT due to the Meissner effect. It is negligible since we use thin films. If it were the Meissner effect the field would get distorted on a length scale of the diameter (~cm) and then two discs hovering above and below each other would affect it other. Which is clearly not the case. The discs are actually trapped in constant field contours rather than levitating."