We present a radio survey of X-ray sources in the Large and Small Magellanic clouds with the Australia Telescope Compact Array at 6.3 and 3.5 cm. Specifically, we have observed the fields of five LMC and two SMC supersoft X-ray sources, the X-ray binaries LMC X-1, X-2, X-3 & X-4, the X-ray transient Nova SMC 1992, and the soft gamma-ray repeater SGR 0525-66. None of the targets are detected as point sources at their catalogued positions. In particular, the proposed supersoft jet source RXJ 0513-69 is not detected, placing constraints on its radio luminosity compared to Galactic jet sources. Limits on emission from the black hole candidate systems LMC X-1 and X-3 are consistent with the radio behaviour of persistent Galactic black hole X-ray binaries, and a previous possible radio detection of LMC X-1 is found to almost certainly be due to nearby field sources. The SNR N49 in the field of SGR 0525-66 is mapped at higher resolution than previously, but there is still no evidence for any enhanced emission or disruption of the SNR at the location of the X-ray source. No radio point sources were detected at any wavelength at the catalogued locations of the target sources. In most cases a noise level of 50 microJy or so was achieved, making the 3-sigma upper limits very stringent indeed. The noise levels for LMC X-1 and SGR 0525-66 are considerably worse, due to their locations in radio-bright regions.