The performance of the grid-based Numerov procedure for the prediction of fundamental as well as the first vibrational overtone has been systematically probed for harmonic and anharmonic model systems. In addition to monitor the prediction with respect to the spacing of the potential grid the influence of higher order approximations to the second derivative (i.e. stencils) in Schrödingers equation is evaluated. The latter enable a significant increase of the grid-spacing to achieve results of similar accuracy obtained with smaller stencil sizes. Application to the hydroxyl vibrational mode of methanol, phenol and the natural product thymol in vacuum and carbon tetrachloride predicted wavenumbers within less than 1% of experiment. Due to the highly localised character of the OH-vibration the ad hoc construction of the associated normal mode yields results of similar accuracy than those obtained using the analytical normal modes, effectively eliminating the requirement of an analytical normal mode evaluation of the entire system. This property was shown to be of particular advantage when considering explicit solute-solvent contacts, which have been demonstrated to be superior compared to an implicit representation of solvent effects. The combination of the observed findings (i.e. enlarged grid-spacing due to the application of higher order stencils, construction of localised normal modes) is envisaged to be of particular benefit when investigating localised modes in large systems, such as OH or NH groups in large (bio)macromolecules or solid-state surfaces.