Accurate data sets including noncovalent interactions have become essential for benchmarking computational methods. However, while there is much focus on obtaining an accurate description of relative energies, reliable prediction of accurate equilibrium geometries is also important. To facilitate the benchmarking of computed geometries, the current work includes an accurate data set of semiexperimental equilibrium geometries of noncovalent complexes that can be directly compared to ab initio data. The structures are based on high accuracy spectroscopic data, combined with vibrational corrections at the double-hybrid density functional level. The current work is designed to complement available data sets of semiexperimental geometries of small rigid molecules and ab initio geometries of complexes. The benchmark-quality data comprises 16 complexes and includes dispersion interactions, hydrogen bonding, CH/pi center dot center dot center dot pi interactions, and trimers. In addition to the reference data, accurate counterpoise-corrected geometries have been obtained up to the CCSD level, along with interaction energies. A short overview of the performance of computational methods, including dispersion-corrected B3LYP and B2PLYP functionals, is also included.