The levitation force between a single grain YBCO cylindrical bulk superconductor and a permanent magnet is investigated. The force measured both in zero field cooling and field cooling condition in the temperature range 20 K - 80 K is reported. The dependence of peak levitation force and power dissipation on the temperature is analyzed and the saturation of the peak force with increasing the critical current of the material is pointed out. A numerical analysis is also carried out for understanding the electrodynamics of the levitation mechanism. Good reproduction of the measured data is obtained and relevant observed phenomena, such as hysteresis of the levitation cycle at high temperature and saturation of the peak force at low temperature, are explained by means of the model. Characterization of the material in terms of critical current density in the field range 0 T - 0.5 T is also obtained by means of the numerical model by means of the fitting of the measured data.