Three-pulse radio-frequency (rf) driven electron spin echo envelope modulation (ESEEM) is introduced as a method to measure hyperfine couplings of electron-nuclear spin systems in liquids. It is distinguished from the corresponding two-pulse experiment by narrower lines. Numerical simulations of rf-driven ESEEM based on Floquet theory are given and compared with average Hamiltonian theory. Artifacts which appear in rf-driven ESEEM spectra are discussed, and approaches for the removal of these artifacts such as time-proportional phase incrementation (TPPI) of the rf phase and an rf phase cycle (0, pi) are presented. The validity of the analytical description of the rf-driven ESEEM experiment is shown by comparison with experimental results.