The method and basis set dependence of zero-point vibrational corrections (ZPVC) to NMR shielding constants and anisotropies has been investigated using water as a test system. A systematic comparison has been made using the Hartree-Fock (HF), second-order Møller-Plesset perturbation theory (MP2), coupled cluster singles and doubles (CCSD), coupled cluster singles and doubles with perturbative triples corrections (CCSD(T)) and Kohn-Sham density functional theory (DFT) with the B3LYP exchange-correlation functional methods in combination with the second order vibrational perturbation theory (VPT2) approach for the vibrational corrections. As basis sets the correlation consistent basis sets cc-pVXZ, aug-ccpVXZ, cc-pCVXZ and aug-cc-pCVXZ with X = D, T, Q, 5, 6 and the polarization consistent basis sets aug-pc-n and aug-pcS-n with n = 1, 2, 3, 4 were employed. Our results show, that basis set convergence of the vibrational corrections is not monotonic and that very large basis sets are needed before a reasonable extrapolation to the basis set limit can be performed. Furthermore, our results suggest that coupled cluster methods and a decent basis set are required before the error of the electronic structure approach is lower than the inherent error of the VPT2 approximation.