An accuracy-controllable alternating-direction implicit finite-difference time-domain method is presented in this paper for the efficient modeling of integrated semi-conductor circuits and printed circuit boards in modern EMC structures. Preserving the formulation of the conventional algorithm, the novel 3-D concept introduces supplementary nodes in terms of a convex stencil procedure in order to significantly suppress the detrimental dispersion errors due to the Courant limit cancellation. Thus, instead of utilizing the typical derivative approximators, a set of weighted interpolating polynomials, which do not increase the overall algorithmic complexity, is derived. Numerical results, obtained for various time-steps, are compared to reference solutions or measurement data, revealing the limitations of existing schemes and the advantages of the proposed technique.