We present new radio continuum observations of two dwarf starburst galaxies, NGC 3125 and 5408, with observations at 4.80 GHz (6 cm) and 8.64 GHz (3 cm), taken with the Australia Telescope Compact Array (ATCA). Both galaxies show a complex radio morphology with several emission regions, mostly coincident with massive young star clusters. The radio spectral indices of these regions are negative (with alpha~-0.5 to -0.7), indicating that the radio emission is dominated by synchrotron emission associated with supernova activity from the starburst. One emission region in NGC 5408 has a flatter index (alpha~-0.1) indicative of optically thin free-free emission, which could indicate it is a younger cluster. Consequently, in these galaxies we do not see regions with the characteristic positive spectral index indicative of optically obscured star formation regions, as seen in other dwarf starbursts such as Hen 2-10.