Semiempirical quantum mechanical (QM) methods with corrections for noncovalent interactions provide a favorable combination of accuracy and computational efficiency that makes them a useful tool for a study of large molecular systems. It was, however, noted that the accuracy of these methods deteriorates at intermolecular distances shorter than equilibrium. In this work, we explore this issue systematically using a newly developed data set of benchmark interaction energies named R160x6. This data set maps repulsive contacts in organic molecules, and it consists of 160 model complexes for which six points along the dissociation curve are provided. Testing a wide range of semiempirical QM methods against the CCSD(T)/CBS benchmark revealed that most methods, and all the dispersion-corrected ones, underestimate the repulsion systematically. The worst cases are usually hydrogen hydrogen contacts. The best results were obtained with PM6-D3H4 and DFTB3-D3H4, as these methods already contain a correction for the H-H repulsion, but the errors are still about twice as large as in equilibrium geometries.