Abstract We examine the central stellar velocity dispersion of subhalos based on IllustrisTNG cosmological hydrodynamic simulations. The central velocity dispersion is a fundamental observable that links galaxies with their dark matter subhalos. We carefully explore simulated stellar velocity dispersions derived with different definitions to assess possible systematics. We explore the impact of variation in the identification of member stellar particles, the viewing axes, the velocity dispersion computation technique, and simulation resolution. None of these issues impact the velocity dispersion significantly; any systematic uncertainties are smaller than the random error. We examine the stellar mass–velocity dispersion relation as an observational test of the simulations. At fixed stellar mass, the observed velocity dispersions significantly exceed the simulation results. This discrepancy is an interesting benchmark for the IllustrisTNG simulations because the simulations are not explicitly tuned to match this relation. We demonstrate that the stellar velocity dispersion provides measures of the dark matter velocity dispersion and the dark matter subhalo mass.