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There have recently been detections of radio emission from low-mass stars,some of which are indicative of star-planet interactions. Motivated by theseexciting new results, in this paper we present Alfv\'en wave-driven stellarwind models of the two active planet-hosting M dwarfs Prox Cen and AU Mic. Ourmodels incorporate large-scale photospheric magnetic field maps reconstructedusing the Zeeman-Doppler Imaging method. We obtain a mass-loss rate of$0.25~\dot{M}_{\odot}$ for the wind of Prox Cen. For the young dwarf AU Mic, weexplore two cases: a low and high mass-loss rate. Depending on the propertiesof the Alfv\'en waves which heat the corona in our wind models, we obtainmass-loss rates of $27$ and $590~\dot{M}_{\odot}$ for AU Mic. We use ourstellar wind models to assess the generation of electron cyclotron maserinstability emission in both systems, through a mechanism analogous to thesub-Alfv\'enic Jupiter-Io interaction. For Prox Cen we do not find any feasiblescenario where the planet can induce radio emission in the star's corona, asthe planet orbits too far from the star in the super-Alfv\'enic regime.However, in the case that AU Mic has a stellar wind mass-loss rate of$27~\dot{M}_{\odot}$, we find that both planets b and c in the system caninduce radio emission from $\sim10$ MHz to 3 GHz in the corona of the host starfor the majority of their orbits, with peak flux densities of $\sim10$ mJy.Detection of such radio emission would allow us to place an upper limit on themass-loss rate of the star.

Planet-induced radio emission from the coronae of M dwarfs: the case of Prox Cen and AU Mic