Iron phosphates (FePO4) are among the most promising candidate materials for advanced Li-ion battery cathodes. This work reports upon a combined nuclear magnetic resonance (NMR) experimental and periodic density functional theory (DFT) computational study of the environments and electronic structures occurring in a range of paramagnetic Fe(III) phosphates comprising FePO4 (heterosite), monoclinic Li3Fe2(PO4)(3) (anti-NASICON A type), rhombohedral Li3Fe2(PO4)(3) (NASICON B type), LiFeP2O7, orthorhombic FePO4 center dot 2H(2)O (strengite), monoclinic FePO4 center dot 2H(2)O (phosphosiderite), and the dehydrated forms of the latter two phases. Many of these materials serve as model compounds relevant to battery chemistry. The P-31 spin-echo mapping and Li-7 magic angle spinning NMR techniques yield the hyperfine shifts of the species of interest, complemented by periodic hybrid functional DFT calculations of the respective hyperfine and quadrupolar tensors. A Curie-Weiss-based magnetic model scaling the DFT-calculated hyperfine parameters from the ferromagnetic into the experimentally relevant paramagnetic state is derived and applied, providing quantitative finite temperature values for each phase. The sensitivity of the hyperfine parameters to the composition of the DFT exchange functional is characterized by the application of hybrid Hamiltonians containing admixtures 0%, 20%, and 35% of Fock exchange. Good agreement between experimental and calculated values is obtained, provided that the residual magnetic couplings persisting in the paramagnetic state are included. The potential applications of a similar combined experimental and theoretical NMR approach to a wider range of cathode materials are discussed.