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There are two ways of treating transient radiation and scattering problems for structures of arbitrary shape: solution of time-dependant Maxwell equations directly in the time domain; solution of these equations in the frequency domain with consequent application of the Fourier transformation to reconstruct the time-dependant signal. Comparative advantages and disadvantages of both approaches are well described in the literature (Poggio, A.J. and Miller, E.K., 1973). The paper aims to increase the effectiveness of the multifrequency approach by performing adaptive frequency sampling (AFS) for spectrum calculation of the electromagnetic system under consideration. The paper demonstrates that the solution of transient problems in the frequency domain with consequent application of FFT becomes very effective if frequency sampling is performed using the AFS technique. Implementation details of the AFS algorithm and examples demonstrating the advantages of applying AFS are also presented.