Abstract Experiments indicating the excitation of whispering gallery-type electromagnetic modes by a vortex moving in an annular Josephson junction are reported. At relativistic velocities the Josephson vortex interacts with the modes of the superconducting stripline resonator giving rise to novel resonances on the current–voltage characteristic of the junction. The coupling between the vortex and the linear modes of the junction is explained using a Cherenkov–radiation-like mechanism. We analytically calculate the spectrum of the linear modes taking into account the electromagnetic environment of the junction. The experimental data are in good quantitative agreement with the analysis and numerical calculations based on the two-dimensional sine-Gordon model.