We present a method to treat scattering of electrons with atomic roughness at interfaces, surfaces, and edges on nanometer-scale structures based on local empirical pseudopotentials. This approach merges the computational advantages of macroscopic models based on the shift of a phenomenological “barrier potential,” with the physical accuracy of models based on modifications of the atomic configuration at the interface/surface/edge. We illustrate the method by considering the dependence of the scattering matrix element on the confinement (inversion) field in free-standing H-terminated Si inversion layers, on the thickness in similarly H-terminated thin-Si bodies, on the diameter of free-standing [100] cylindrical Si nanowires, and on the width of armchair-edge graphene nanoribbons. For these latter structures, we find extremely large scattering rates, whose magnitude — ultimately due to the chirality dependence of the bandgap — renders perturbation theory invalid and prevents us from drawing quantitative conclusions about transport properties. Yet, they show clearly the dominant role played by line-edge roughness in controlling electronic transport in these structures, in agreement with suggestions that transport in narrow and rough ribbons does not occur via extended Bloch states.