Unipolar induction (UI) is a fundamental physical process, which occurs when a conducting body transverses a magnetic field. It has been suggested that UI is operating in RX J0806+15 and RX J1914+24, which are believed to be ultra-compact binaries with orbital periods of 5.4 min and 9.6 min respectively. The UI model predicts that those two sources may be electron cyclotron maser sources at radio wavelengths. Other systems in which UI has been predicted to occur are short period extra-solar terrestrial planets with conducting cores. If UI is present, circularly polarised radio emission is predicted to be emitted. We have searched for this predicted radio emission from short period binaries using the VLA and ATCA. In one epoch we find evidence for a radio source, coincident in position with the optical position of RX J0806+15. Although we cannot completely exclude that this is a chance alignment between the position of RX J0806+15 and an artifact in the data reduction process, the fact that it was detected at a significance level of 5.8 sigma and found to be transient, suggests that it is more likely that RX J0806+15 is a transient radio source. We find an upper limit on the degree of circular polarisation to be ~50%. The inferred brightness temperature exceeds 10^18 K, which is too high for any known incoherent process, but is consistent with maser emission and UI being the driving mechanism. We did not detect radio emission from ES Cet, RX J1914+24 or Gliese 876.