The levitation force between a permanent magnet and a superconducting thin film was investigated experimentally. The configuration consisted of a cylindrical NdFeB permanent magnet placed above a circular YBa2Cu3O7−δ disk with common cylinder axis. Precise measurements were made of the vertical force Fz and the magnetic stiffness κz as a function of the magnet–superconductor separation at 77 K. Several features contrasting the levitation force produced using bulk superconductors were observed. Thin films produced very high values for Fz and κz per unit volume of superconducting material. The hysteretic behavior of Fz during decreasing and increasing separation resulted in loops of nearly symmetrical shape, which also contain a peak in the repulsive force branch. The observations are analyzed and explained with good quantitative agreement using recent theories for flux penetration in thin superconductors in transverse magnetic fields.