We systematically investigate the effects of having Pt as a substrate and/or capping layer on the magnetism and magnetocrystalline anisotropy (MCA) of 3d transition metal (TMs; Cr, Mn, Fe, and Co) monolayers (MLs) by using a first-principles calculationl method. We found that Fe and Co MLs are ferromagnetic (FM) on a Pt(001) surface, but Mn and Cr MLs are antiferromagnetic (AFM). The magnetic moments are quite robust with additional Pt-capping. Furthermore, Pt-capping enhances the small perpendicular MCA (meV) of Fe/Pt(001) significantly to 4.44 meV. Our electronic structure analyses indicate that strong hybridization between Pt-5d and TM-3d orbitals plays a crucial role in determining magnetic ordering and MCA. For comparison we also calculated magnetism and MCA of 3d TM MLs on Ta(001) with and without Ta-capping.