The solar radio noise accurately measured by terrestrial solar observatories has been proved to be an effective reference for checking the quality of dual-polarization weather radar receivers. The longest, most complete and accurate record of solar spectral irradiance ("flux", for the sake of brevity) values exists thanks to the Dominion Radio Astrophysical Observatory (DRAO) of the National Research Council (NRC) of Canada, located in British Columbia. Solar flux measurements acquired by DRAO at 2.8 GHz represent a valuable and useful basis for the calibration of radar receivers. In Europe the large majority of weather radars operates between 5.4 and 5.6 GHz. To be rigorous, one needs measurements of solar radio noise at the same frequency of the weather radar. If one is prepared to accept some uncertainty, it is possible to extrapolate solar flux values from S- to C-band. The formula proposed by Tapping (2001) is widely used in Europe: it is based on a constant scaling factor to predict the flux at the higher frequency from the measured flux at 2.8 GHz, after having subtracted the quiet component at both frequencies. We have analyzed 240 quality-checked, 1-hour lasting solar flux measurements, simultaneously acquired at S- and C-band by the Expanded Owens Valley Solar Array (EOVSA) observatory during the current XXV solar cycle and empirically derived the optimal value of the scaling factor for the conversion from S- to C-band. We found that there is a clear non-linear dependence between this variable scaling factor and the slowly varying solar component. Thanks to the new conversion formula, which is based on the variable scaling factor, the agreement between C-band radar observations in Europe and DRAO-converted reference values improved both in relative and in absolute terms. Not much can be done to compensate the shift in time between measurements in Europe vs DRAO (noon at 20 UTC). Our recommendation is that of developing and installing an optimized C-band radio telescope in Europe tailored to radar calibration purposes.