The modeling of superconducting magnetic bearings (SMBs) is of great significance for predicting and optimizing their levitation performance before construction. Although much effort has been made in this area, there still remains some space for improvements. Thus the goal of this work is to report a flexible, fast and trustworthy H-formulation finite element model. First the methodology for modeling and calibrating both bulk-type and stack-type SMBs is summarized. Then its effectiveness for simulating SMBs in 2D, 2D axisymmetric and 3D is evaluated by comparison with measurements. In particular, original solutions to overcome several obstacles are given: clarification of the calibration procedure for stack-type and bulk-type SMBs, details on the experimental protocol to obtain reproducible measurements, validation of the 2D model for a stack-type SMB modeling the tapes' real thickness, implementation of a 2D axisymmetric SMB model, implementation of a 3D SMB model, and extensive validation of the models by comparison with experimental results for field cooling and zero field cooling, for both vertical and lateral movements. The accuracy of the model being having proven, it now has a strong potential for speeding up the development of numerous applications including maglev vehicles, magnetic launchers, flywheel energy storage systems, motor bearings and cosmic microwave background polarimeters.