We calculate the broad-band radio–X-ray spectra predicted by microblazar and microquasar models for ultraluminous X-ray sources (ULXs), exploring the possibility that their dominant power-law component is produced by a relativistic jet, even at near-Eddington mass accretion rates. We do this by first constructing a generalized disc–jet theoretical framework in which some fraction of the total accretion power, Pa, is efficiently removed from the accretion disc by a magnetic torque responsible for jet formation. Thus, for different black hole masses, mass accretion rates and magnetic coupling strength, we self-consistently calculate the relative importance of the modified disc spectrum, as well as the overall jet emission due to synchrotron and Compton processes. In general, transferring accretion power to a jet makes the disc fainter and cooler than a standard disc at the same mass accretion rate; this may explain why the soft spectral component appears less prominent than the dominant power-law component in most bright ULXs. We show that the apparent X-ray luminosity and spectrum predicted by the microquasar model are consistent with the observed properties of most ULXs. We predict that the radio synchrotron jet emission is too faint to be detected at the typical threshold of radio surveys to date. This is consistent with the high rate of non-detections over detections in radio counterpart searches. Conversely, we conclude that the observed radio emission found associated with a few ULXs cannot be due to beamed synchrotron emission from a relativistic jet.