The frequency shift of the proton donor in hydrogen bonded complexes is an important quantity which enables to discuss the nature of the hydrogen bond. Calculations of frequency shifts by quantum chemical methods are usually performed within the harmonic approximation and therefore the comparison with experimental data is biased. We have investigated the importance of anharmonic corrections in the case of twelve complexes in which either FH or ClH is the proton donor. Hartree-Fock, Moller-Plesset second and third order (MP2, MP3), density functional theory (DFT), and hybrid Hartree-Fock/DFT methods have been used for the calculations. It is shown that the anharmonic contribution to the frequency shift is rather method dependent. Its magnitude is usually 10%-20% of the total shift though it can be as large of similar to 50% for (ClH)(2). Once anharmonicity is taken into account, most methods tend to noticeably overestimate the frequency shifts. In the case of DFT related approaches this trend is interpreted in terms of a poor description of the exchange in the intermolecular region.