We present the first systematic investigation of shifts in the nuclear magnetic resonance (NMR) shielding constant due to hydrogen bonding using either the series of wave function based methods, Hartree-Fock (HF), second-order Møller-Plesset perturbation theory (MP2), Coupled Cluster Singles and Doubles (CCSD) and CCSD extended with an approximate description of triples (CCSD(T)), or Density Functional Theory (DFT) employing either the B3LYP, PBE0, or KT3 exchange correlation (xc) functionals. The molecular systems considered are (i) the water dimer and (ii) formaldehyde in complex with two water molecules. Specially for the (17)O in formaldehyde we observe significant differences between the DFT and CCSD(T) predictions. However, the extent of these deviations depends crucially on the applied xc functional. Compared to CCSD(T) we find the KT3 functional to provide accurate results, whereas both B3LYP and PBE0 are in significant error. Potential consequences of this observation are discussed in the context of general predictions of NMR shielding constants in condensed phase.