The error of asymptotic waveform evaluation (AWE) is estimated by the error analysis of rational approximation, and an efficient bandwidth estimation approach is finally proposed, which is used to form a new adaptive frequency-sweep analysis algorithm for a given frequency band in this paper. The broadband electromagnetic scattering analysis of three-dimensional (3-D) perfectly electrically conducting (PEC) objects with different shapes is performed, and dispersive dielectric object is considered. The effectiveness of the proposed method is proved by comparing the numerical results with those obtained from the analytical solution and the direct solution.