IIRC, it was the iron in the hemoglobin in the blood that was reacting to the magnetic field...
I believe the frog levitation relied on a property of materials called diamagnetism. This is a weak repulsive force that is not the same as ferromagnetism (the strong magnetic property of iron-like materials). I seem to recall that they also levitated strawberries, which have no hemoglobin, but do have water, which is diamagnetic.) Unfortunately, extremely strong magnetic fields are required for this technique, so it's not so practical for levitating larger objects.
I believe the levitating coins is based on a third type of magnetism. Oxygen is paramagnetic, meaning that it is weakly attracted to a magnetic field. In this experiment they appear to have induced a density/pressure gradient in high pressure oxygen using a strong magnetic field. The coins then float at this gradient.