This manuscript focuses on the degrading effects of discretization errors on the simulation results of strongly coupled models. Coupled simulation models, be they multi-scale or multi-physics in nature, in recent years, have gained significant attention for their ability to predict the behavior of complex physical systems by implementing mature, independently developed, constituent models. This investigation evaluates the numerical errors inherent in the predictions of the constituent models and their effects on the predictions of the coupled model. Not only are the discretization errors of each constituent model quantified as they propagate from one constituent to the other during coupling iterations, but their effects on the computational requirements of the coupling procedure are also considered. Furthermore, the sensitivity of the coupled model predictions to each constituent is determined allowing a thorough evaluation of the impact of discretization errors on coupled model predictions. These relationships are demonstrated through a case study of a strongly coupled dynamical system.