ABSTRACT The presence and detectability of coherent radio emission from compact binary mergers (containing at least one neutron star) remains poorly constrained due to large uncertainties in the models. These compact binary mergers may initially be detected as short gamma-ray bursts or via their gravitational wave emission. Several radio facilities have developed rapid response modes enabling them to trigger on these events and search for this emission. For this paper, we constrain this coherent radio emission using the deepest available constraints for GRB 150424A, which were obtained via a triggered observation with the Murchison Widefield Array. We then expand this analysis to determine the properties of magnetar merger remnants that may be formed via a general population of binary neutron star mergers. Our results demonstrate that many of the potential coherent emission mechanisms that have been proposed for such events can be detected or very tightly constrained by the complementary strategies used by the current generation of low-frequency radio telescopes.