We present a robust approach for quantitative precipitation estimation (QPE) for water resources management in mountainous catchments, where rainfall sums and variability are correlated with orographic elevation, but density of rain gauges does not allow for advanced geostatistical interpolation of rainfall fields. Key of the method is modelling rainfall at unobserved locations by their elevation-dependent expected daily mean, and a daily fluctuation which is determined by spatial interpolation of the residuals of neighbouring rain gauges, scaled according to the elevation difference. The scaling factor is defined as the ratio of covariance and variance, in analogy to the “beta” used in economics. The approach is parameterized and illustrated for the Chirilu catchments (Chillón, Rímac, Lurín) in the Andes near Lima, Peru. The results are compared to conventional IDW (inverse-distance weighting) interpolation and a merged national rainfall product. The method results in QPE that are better matching with observed discharges. The combination of inverse-distance weighting with β-scaling thus provides a robust and flexible means to estimate rainfall input to mesoscale mountainous catchments.