Quantitative treatment of the problems related to scanning electrochemical microscopy (SECM) is performed by means of numerical simulations using the boundary element method (BEM). The method is used to calculate the amperometric steady-state response of a microelectrode or nanoelectrode of a given arbitrary geometry in the SECM feedback mode above surfaces with ideal negative feedback or diffusion-controlled positive feedback. By changing the problem setup from the interior to the exterior Laplace formalism, the precision of the c I calculation could be improved significantly because the exterior formulation does not require any assumptions about the extension of the diffusion layer at infinite time. The improved precision was demonstrated by simulations of standard problems that have been treated before by finite difference methods. Subsequently a series of simulations is presented that explores the effects of deviations from idealized SECM geometries used in many available finite difference simulations. Such deviations from ideal geometries are frequently encountered in routine SECM experiments and exert a varying influence on the precision of the obtained data and derived physicochemical parameters. Because of the speed of calculation and the flexibility of the geometric arrangements, entire SECM line scans were simulated and used to analyzed some issues of recently introduced SECM instruments with integrated distance control mechanisms.