The performance of different DFT (UDFT-IGLO, UDFT-GIAO, SOS-DFPT-IGLO) and hybrid-DPT approaches, as well as of HF-GIAO and MP2-GIAO methods has been compared for the calculation of O-17 chemical shielding in the series of tetrahedral d(0) oxo complexes : MO4(M=Fe,Ru,Os), MO4-(M=Mn,Tc,Re), and MO42-(M=Cr,Mo,W). While HF-GIAO and MP2-GIAO fail for systems with low-lying excited states (e.g., MnO4-, CrO42-, or MO4), the DFT methods consistently remain remarkably stable. Larger basis sets change the results little, SOS-DFPT correction terms are small, and differences between different local and gradient-corrected exchange-correlation functionals are also minor. The inclusion of CHF-type coupling terms for DFT-HF hybrid; functionals leads to a significant overestimate of the paramagnetic contributions, the neglect of these terms to an equally large underestimate. DFT-IGLO results for the 3d complexes show an unexpectedly large dependence on whether the metal semicore shells are localized separately or together with the valence orbitals. In this context, the Pipek-Mezey localization scheme appears to be more stable than the more common Boys localization. The origin of the large scalar relativistic effects found for the 5d complexes is discussed by comparing results for the shielding tensors obtained with quasirelativistic and with nonrelativistic metal ECPs. Periodic trends are analyzed in terms of MO contributions to the shielding tensors.