Microwave links can be used to estimate the path-averaged rain rate along the link when precipitation occurs. They take advantage of the near proportionality between the specific attenuation affecting the link signal and the rain rate. This paper deals with the influence of the spatial variability of rainfall along the link on the accuracy of the rainfall estimates. We focus on single-polarization single-frequency links operating at frequencies ranging from 5 to 50 GHz and with path lengths ranging from 500 m to 30 km. A stochastic simulation framework is used to investigate the frequency at which the linearity occurs (found to be about 30 GHz) for intense Mediterranean precipitation. In addition, the error associated with path-averaged rain rate estimates is being quantified. For instance, the bias is found to be in the order of -15% with an uncertainty of about 10% for microwave links described in the recent literature.