A simple method is given for using a fast but not necessarily accurate scattering approximation to interpolate the results of an exact calculation. The goal is to minimize the number of points where the expensive, exact calculation must be done. The approximate theory is used to remove the rapidly varying parts of the exact S-matrix to obtain a slowly varying correction matrix which can then be interpolated over a large interval in energy or angular momentum. After the interpolation, the rapidly varying approximate parts are put back in to give an accurate S-matrix. The method preserves the phase of the S-matrix. It is demonstrated for the cases of symmetric molecular charge exchange and for rotationally inelastic scattering.