The harmonic and anharmonic frequencies of fundamental vibrations in formaldehyde and water were successfully estimated using the B3LYP Kohn-Sham limit. The results obtained with polarization- and correlation-consistent basis sets were fitted with a two-parameter formula. Anharmonic corrections were obtained by a second order perturbation treatment (PT2). We compared the performance of the PT2 scheme on the two title molecules using SCF, MP2 and DFT (BLYP, B3LYP, PBE and B3PW91 functionals) methods combined with polarization consistent pc-n (n = 0, 1, 2, 3, 4) basis sets, Dunning's basis sets (aug)-cc-pVXZ where X = D, T, Q, 5, 6 and Pople's basis sets up to 6-311++G(3df,2pd). The influence of SCF convergence level and density grid size on the root mean square of harmonic and anharmonic frequency deviations from experimental values was tested. The wavenumber of formaldehyde CH(2) anharmonic asymmetric stretching mode is very sensitive to grid size for large basis sets; this effect is not observed for harmonic modes. BLYP-calculated anharmonic frequencies consistently underestimate observed wavenumbers. On the basis of formaldehyde anharmonic frequencies, we show that increasing the Pople basis set size does not always lead to improved agreement between anharmonic frequencies and experimental values.