Nuclear Magnetic Resonance (NMR) spectroscopy of paramagnetic solids represents an exceptional means for getting insight into structural and electronic properties of the systems, giving on the other hand a particularly involved response to analyse. Specifically, the overall isotropic shift is given by a combination of the Fermi contact term, dependent on the electronic structure of the paramagnetic site and on the strength and covalency of its bond with the observed centre, and on the pseudo-contact term, a relativistic dipolar  contribution that gives information regarding the structure and the spatial arrangements of the sites in the system. In this work we present a protocol to extend the computation of the paramagnetic shielding in the presence of spin-orbit coupling towards solid systems, with which to calculate these two contributions explicitly via periodic solid-state Density Functional Theory (DFT) so to unravel detailed information hidden in the NMR spectrum. We describe how the involved properties such as g- and hyperfine tensors behave in paramagnetic solids where the spin-bearing ions are a major constituent of the crystal lattice. Finally it is clarified how to combine these quantities in order to separate the various terms contributing to the paramagnetic shielding, σ^s : this method enables to get deeper insight into the overall isotropic shift and shift anisotropy observed experimentally, and to identify information regarding electronic structure and geometry of the system. The method is applied to a series of solid-state LiTMPO₄ (with TM=Mn, Fe, Co and Ni) powders and the corresponding ⁷Li and ³¹P NMR shifts are computed. From these results we outline differences in the extent of spin-orbit coupling effects and electron-nuclear magnetic interaction, and the various tensorial products are combined together to explicitly calculate all the terms involved in the description of σ^s . A detailed comparison is presented between contact and dipolar interactions within the same system and across the series, to untangle the dual nature of the overall isotropic shift and shift anisotropy.