The validation of algorithms which are used for the evaluation of geometric measurands of products provides an important and economically advantageous supplement to the calibration of multidimensional coordinate measuring machines. This work describes mathematical procedures for an acceptance test of relevant evaluation results. The underlying applications from coordinate metrology comprise optimal fitting of geometric elements according to the Chebyshev, minimum circumscribed and maximum inscribed criteria as well as three-dimensional hole pattern fitting. These are represented by constrained non-linear minimization programs. Based on metrological needs, test data sets are classified according to their reliability for the validation of software beyond existing mathematical concepts. Test data sets with the necessary requirements are created by a newly developed inverse data generator. In addition, numerical uncertainties are calculated for the reference fitting results associated with the test data. These are essential for an assessment of the test quality and the range of accuracy. Such a detailed evaluation of the accuracy of test data is less common in many mathematical applications. iv