We propose a method based on surface-enhanced Raman scattering (SERS) to estimate the resonance Raman cross sections of dyes. The latter are notoriously difficult (or impossible) to obtain by normal (spontaneous) constant wave Raman spectroscopy when the fluorescence quantum yield of the molecules is good and the overwhelming effect of fluorescence masks the Raman spectrum. We propose here to use the fluorescence quenching occurring in SERS conditions to overcome simply this problem. The principles of the method are described and its limitations discussed in detail. The method is demonstrated by estimating the resonance Raman differential cross sections for Rhodamine 6G for seven different excitation wavelengths across the visible range.