The atmospheric precipitable water vapour content (PWV) strongly affects astronomical observations in the infrared (IR). We have validated the Weather Research and Forecasting (WRF) mesoscale numerical weather prediction (NWP) model as an operational forecasting tool for PWV. In the validation, we used atmospheric radiosounding data obtained directly at the Roque de los Muchachos Observatory [ORM: ≈2200 metres above sea level (masl)] during three intensive runs and an aditional verification sample of 1 yr of radiosonde data from World Meteorological Organization (WMO) station 60018 in Güímar (Tenerife, TFE: ≈105 masl). These data sets allowed us to calibrate the model at the observatory site and to validate it under different PWV and atmospheric conditions. The ability of the WRF model in forecasting the PWV at astronomical observatories and the effects of horizontal model grid size on the computed PWV and vertical profiles of humidity are discussed. An excellent agreement between model forecasts and observations was found at both locations, with correlations above 0.9 in all cases. Subtle but significant differences between model horizontal resolutions have been found, the 3 km grid size being the most accurate and the one selected for future work. Absolute calibrations are given for the lowest and finest grid resolutions. The median PWV values obtained were 3.8 and 18.3 mm at ORM and TFE, respectively. WRF forecasts will complement the PWV measured by the GPS monitoring system at the Canarian Observatories.