Context. Runaway stars produce bowshocks that are usually observed at infrared (IR) wavelengths. Non-thermal radio emission has been detected so far only from the bowshock of BD+43°3654, whereas the detection of non-thermal radiation from these bowshocks at high energies remains elusive. Aims. We aim at characterising in detail the radio, X-ray, and γ-ray emission from stellar bowshocks accounting for the structure of the region of interaction between the stellar wind and its environment. Methods. We develop a broadband-radiative, multi-zone model for stellar bowshocks that takes into account the spatial structure of the emitting region and the observational constraints. The model predicts the evolution and the emission of the relativistic ...