We introduce a new method for expanding equivalent surface current densities over open surfaces. The new method is based on the equivalence principle, which is theoretically used with closed surfaces. Utilizing low-order basis functions to compute the expansion coefficients of equivalent surface currents and then weighting these coefficients with an appropriate window function compensates for computational field errors originating from using truncated currents at the open boundaries. These modified coefficients can be used to reproduce the original electromagnetic fields inside a limited equivalent region. The simulations demonstrate that relative errors as low as 1-2.5% are achievable based on the specifics of the source and shape of the open surface. © 2014 IEEE.