Magnetic levitation and stiffness have been measured in several systems composed of a permanent magnet elastically suspended above a stationary melt‐textured sample of Y‐Ba‐Cu‐O. The levitation force and vertical stiffness have been calculated on the basis of magnetization measurements of the same system, and the calculated results showed excellent agreement with the experimental measurements. Based on the force and magnetization measurements, it is predicted that the same Y‐Ba‐Cu‐O material configured in a geometry suitable for magnetic bearings could produce a levitation pressure of 100–400 kPa at 20 K.