We have investigated the performance of the most popular relativistic density
functional theory methods, zeroth order regular approximation (ZORA) and 4-component Dirac-Kohn-Sham (DKS), in the calculation of the recently measured
hyperfine coupling constants of ReIV and IrIV in their hexafluorido ions. We find that both methods lead to very similar deviations from the experimental values for the [ReF₆]^2- complex, i.e. ~20% for the coupling constant using hybrid functionals. None of the methods is, however, able to reproduce the large anisotropy of the [ReF6]2- hyperfine tensor. For [IrF₆]^2- the ZORA method with a variational treatment of spinorbit coupling and the DKS method reproduce the experimental tensor components
with deviations of ~10% and ~5% for the hybrid functionals, while the ZORA method with a perturbational treatment of spin-orbit coupling wrongly predicts the coupling constant to be around one order of magnitude too large. The reasons for this failure and the basis set and functional dependence of the results are discussed. In addition the manuscript presents for the first time detailed equations for the calculation of hyperfine couplings within the DKS approach as implemented in the Respect program.