Basin modeling as a quantitative tool in petroleum studies necessarily implies knowledge about the limiting factors of the model, especially because modeling methods are widely used when ranking exploration targets and assessing associated geologic risk. Commonly, model validity is checked by time-consuming (trial and error) calibrations against measured data, attempting complicated modifications of the model to satisfy the highly nonlinear relationships between model parameters. These procedures can result in an over-interpretation of model results. Inversion procedures, however, aim at finding the simplest set of model parameters that best agree with calibration data, taking the known uncertainties into account. In this article, an easy to use and rapid pseudoinverse method is presented for one-dimensional (1-D) deterministic forward models. By assessing uncertainties and some measure of the goodness of fit to observed data, in this case vitrinite reflectance, the significance of variations of different input parameters can be rapidly evaluated. The method is illustrated on a data set from a detailed 1-D modeling study of a small region of the German Variscan Rhenish massif. The significance and uncertainties of the two main parameters affecting vitrinite reflectance, that is, heat flow and burial depth during maximum burial, are assessed and discussed. Besides using real data, a theoretical approach is presented, by approximating the residual surface using a polynomial or cubic spline interpolation for a few data points only. The resolution limits, sensitivity, and uncertainty can be easily assessed, and the residual surface can be converted to a pseudoprobability density function for use in later risking procedures.