The long time self-diffusion of highly charged colloidal particles consisting of polybutylacrylate was studied employing pulsed field gradient NMR (PFGNMR) and Brownian dynamics (BD) simulations. The potential parameters for the Yukawa interaction potential used in the BD simulations were derived from the static structure factor measured by means of light scattering. The long time self-diffusion coefficients resulting from NMR and BD were compared for different ionic strengths, which cause a screening of the interaction potential due to stray ions. Increasing the ionic strength of the colloidal suspensions, we observed a phase transition from a crystalline to a liquidlike structure. Whereas at high salt concentrations both long time diffusion coefficients agree within a few percent, at intermediate ionic strengths the values measured via PFGNMR are by a factor of 2 higher than those predicted by the BD simulation. This deviation is explained by hydrodynamic interactions which are expected to enhance long time self-diffusion and which are not taken into account in our BD algorithm.