In this work we compute high-coverage hydrogen adsorption energies and geometries on the stepped platinum surfaces Pt(211) and Pt(533) which contain a (100)-step type and the Pt(221) and Pt(553) surface with a (111) step edge. We discuss these results in relation to ultra-high-vacuum temperature programmed desorption (TPD) data to elucidate the origin of the desorption features. Our results indicated that on surfaces with a (100)-step type, two distinct ranges of adsorption energy for the step and terrace are observed, which mirrors the TPD spectra for which we find a clear separation of the desorption peaks. For the (111) step type, the TPD spectra show much less separation of the step and terrace features, which we assign to the low individual adsorption energies for H atoms on this step edge. From our results we obtain a much clearer understanding of the surface-hydrogen bonding at high coverages and the origin of the different TPD features present for the two step types studied.