One of the main issues preventing a large-scale exploration of the full potential of memristors in electrical circuits lies in the convergence issues and numerical errors encountered in the computer-aided integration of the differential algebraic equation set governing the peculiar dynamical behavior of these nonlinear two-terminal electrical components. In most cases the complexity of this equation set prevents an analytical derivation of closedform state solutions. Therefore the investigation of the nonlinear dynamics of memristors and circuits based upon them relies on software-based integration of the mathematical equations. In this paper, we highlight solution accuracy issues which may arise from an improper numerical integration of the equations, and then propose techniques addressing the problems properly. These guidelines represent a useful guide to engineers interested in the numerical analysis of memristor models.