A numerical approximation of the critical values of Cramér-von Mises (CvM) tests is proposed for testing the correct specification of general conditional location parametric functionals. These specifications include conditional mean and quantile models. This method is based on estimation of the eigenelements of the covariance operator associated with the CvM test, and it has the advantage that it requires the practitioner to estimate the model only one time under the null hypothesis. A Monte Carlo experiment shows that the proposed approximation compares favorably with respect to the subsampling method in terms of size accuracy, power performance and computational time.