The mechanism of gyroresonant scattering of charged particles by small-amplitude, broadband electromagnetic waves is examined. By means of quasi-linear theory, a simple expression for the resonant pitch-angle diffusion coefficient $D_{\alpha \alpha}$ is developed, which is valid for parallel-propagating, small-amplitude, (R-mode or L-mode) electromagnetic waves of general spectral density. We calculate the average diffusion coefficient with respect to the pitch-angle $\alpha$, namely $\langle D_{\alpha\alpha}\rangle$, which provides a practical estimate for particle scattering rates as a function of particle kinetic energy. The results for $\langle D_{\alpha\alpha}\rangle$, corresponding to a Gaussian wave frequency spectrum, are used to estimate scattering rates for several types of wave–particle interactions in the terrestrial and Jovian magnetospheres.