The method of asymptotic waveform evaluation (AWE) is applied to the combined-field integral equation (CFIE) to achieve fast and accurate frequency-sweep calculations of electromagnetic scattering and radiation by three-dimensional conducting and dielectric objects. The employment of the CFIE eliminates the interior resonance problem suffered by both the electric-field integral equation and the magnetic-field integral equation. It is shown that the use of AWE can speed up the calculation by more than an order of magnitude. It is also shown that when combined with the complex frequency hopping technique, the AWE method can produce an accurate solution within a prespecified frequency band. Numerical examples are presented to demonstrate the performance of the proposed method. ¿ 1999 American Geophysical Union