A general method for fitting experimental electron paramagnetic resonance spectra to numerically simulated multiparameter model spectra has been developed. The goal of this work is to provide a quantitative and reliable method for evaluating spectral simulations and extracting the maximum information possible from experimental EPR spectra. The calculation involves a minimization of gx2, in which a downhill simplex algorithm is used as the search procedure for varying the parameters that determine the simulated model spectra. This method is applied to determine (1) magnetic tensors and linewidths from spectra of randomly oriented (powder) samples, (2) complex orientational distributions from spectra of oriented assemblies, and (3) exponential recovery times in time-domain EPR. The reliability of the calculation was verified by successful applications to simulated spectra for which the correct results were known, and by showing that the same results were obtained independently of initial assumptions or the convergence path followed, for both simulated and experimental spectra. Estimates of uncertainties in the fitted parameters were obtained by determining the standard deviations from multiple independent calculations with different initial values.