Timing measurements of periodic X-ray pulses from two ultrashort-period double degenerate binaries, RX J1914+24 and RX J0806+15, show that the rates of change of their orbital periods are consistent with gravitational radiation losses. This contradicts the predictions of models which invoke mass transfer between the two white dwarfs. The X-ray emission is, therefore, unlikely to be powered by accretion processes. The unipolar inductor model explains the source of X-ray emission as electrical dissipation at the base of a flux tube, which connects the magnetic white dwarf to its companion. This model is most consistent with the observed X-ray pulse properties. A similar current system exists in the Jupiter–Io system, where a mildly relativistic electron current produces an auroral footprint at the base of the Io flux tube and highly polarized beamed radio emission by means of the electron cyclotron maser mechanism. Detection of radio emission from RX J1914+24 and RX J0806+15 would thus provide further support for the unipolar inductor model. We present theoretical predictions, based on a loss-cone-driven electron cyclotron maser model, of radio fluxes from systems with parameters similar to RX J1914+24 and RX J0806+15.