Polycrystalline bis(dialkyldithiophosphato)Pt(II) complexes of the form [Pt{S2P(OR)(2)}(2)] (R = ethyl, iso-propyl, iso-butyl, sec-butyl or cyclo-hexyl group) were studied using solid-state P-31 and Pt-195 NMR spectroscopy, to determine the influence of R to the structure of the central chromophore. The measured anisotropic chemical shift (CS) parameters for P-31 and Pt-195 afford more detailed chemical and structural information, as compared to isotropic CS and J couplings alone. Advanced theoretical modeling at the hybrid DFT level, including both crystal lattice and the important relativistic spin orbit effects qualitatively reproduced the measured CS tensors, supported the experimental analysis, and provided extensive orientational information. A particular correction model for the non negligible lattice effects was adopted, allowing one to avoid a severe deterioration of the Pt-195 anisotropic parameters due to the high requirements posed on the pseudopotential quality in such calculations. Though negligible differences were found between the Pt-195 CS tensors with different substituents R, the P-31 CS parameters differed significantly between the complexes, implying the potential to distinguish between them. The presented approach enables good resolution and a detailed analysis of heavy element compounds by solid-state NMR, thus widening the understanding of such systems.