The amplification of fluorescence light of an active medium in a Fabry-Perot resonator, transversely pumped with picosecond pulses, is exploited to determine the effective stimulated emission cross-section spectrum, sigma(em,eff)(lambda). A theory is presented for the ratio of amplified fluorescence output to spontaneous emission signal (resonator mirrors removed). The detection sensitivity is enhanced by the multi-pass amplification. Its dependence on the output mirror reflectivity and residual ground-state absorption in the emission region is analysed. As an example the effective stimulated emission cross-section spectrum of coumarin 2 in methanol is measured in the wavelength region 435 nm to 610 nm.