Superconductors will typically levitate if placed above a magnet, and vice versa. Magnets are weird--superconductors even more so. I assume that's what they were referring to?
Edit: Judging by Fig 4, which has a large object conspicuously labeled "magnet", that's probably what they're referring to.
This whole experiment is quite reminiscent of an experiment I did in high school. We synthesized a high temperature superconductor (IIRC it was YBCO) by grinding some powders together with a mortal and pestle and baking the result. And we stuck it in a little cup of LN2 and floated a magnet on it. It really works!
This group used somewhat nastier powders, they had to cook parts of it in a vacuum, and they floated the result on a magnet instead of vice versa. And it only floated a bit. But they did it without any cooling!
Edit: Judging by Fig 4, which has a large object conspicuously labeled "magnet", that's probably what they're referring to.