We report on NMR spectroscopy, CAS-based method calculations, and X-ray diffraction of AnV and AnVI complexes with a neutral and slightly flexible TEDGA ligand. After checking that pNMR shifts mainly arise from pseudocontact interactions, we analyze pNMR shifts considering the axial and rhombic anisotropy of the actinyl magnetic susceptibilities. The results are compared to those of a previous study performed on [AnVIO2]2+ complexes with dipicolinic acid. It is shown that 5f2 cations (PuVI and NpV) make very good candidates for determining the structure of actinyl complexes in solution by 1H NMR spectroscopy as shown by the invariance of the magnetic properties to the equatorial ligands, as opposed to the NpVI complexes with a 5f1 configuration.