We calculate the absorptive part of the frequency-dependent conductivity for a large class of anisotropic superconductors. The effect of nonmagnetic impurity scattering is included at the level of a self-consistent t-matrix approximation. It is found that low-frequency absorption (0 < Ω < 2Δ) takes place for any superconducting state with nodes of the energy gap on the Fermi surface. We demonstrate that the limiting low-frequency dependence of σ(Ω) on impurity concentrations can help to determine the structure of the order parameter in candidate systems such as heavy-electron compounds or high-Tc superconductors. We also discuss how strong scattering, similar to that observed in ordinary superconductors doped with Kondo impurities, may lead to absorption with a threshold of Ω ≈ Δ rather than 2Δ as in quasiisotropic systems. Finally, we consider the contribution of order-parameter collective modes to the electromagnetic absorption, and show that this absorption may be substantial and depends sensitively on the impurity scattering rate.