The assignment of NMR spectra of paramagnetic species (PNMR) can be a complex undertaking because the presence of unpaired electron spins can cause unpredictable changes in the chemical shifts. The use of quantum chemical methods to assist in the assignment of chemical shifts can potentially provide a valuable tool. Many lanthanide and actinide complexes exhibit open shell electronic configurations and their intricate electronic structures can present severe challenges for quantum chemistry. In this work we report, principally, the proton isotropic shifts for a number of complexes containing a single ion with an f¹ electronic configuration. We also touch on preliminary studies of ¹³C and ²⁹Si chemical shifts in systems containing an f³ ion. We employ a methodology based on the computation of spin Hamiltonian parameters and show that it can provide reliable agreement with experimental assignments, and be used to aid the interpretation of experimental PNMR data for f-element compounds. We also show how the formalism can be decomposed to identify and quantify the mechanisms of the paramagnetic effects on the observed spectra, and by doing so offer insight into structure and bonding properties.