The emission from shock breakouts (SBOs) represents the earliest electromagnetic (EM) signal emitted by cataclysmic events involving the formation or the merger of neutron stars (NSs). As such, SBOs carry unique information on the structure of their progenitors and on the explosion energy. The characteristic SBO emission is expected in the UV range, and its detection is one of the key targets of the ULTRASAT satellite. Among SBO sources, we focus on a specific class involving the formation of fast-spinning magnetars in the core-collapse of massive stars. Fast-spinning magnetars are expected to produce a specific signature in the early UV supernova light curve, powered by the extra spin energy quickly released by the NS. Moreover, they are considered as optimal candidates for the emission of long-transient gravitational wave (GW) signals, the detection of which requires early EM triggers to boost the sensitivity of dedicated GW search pipelines. We calculate early supernova UV light curves in the presence of a magnetar central engine, as a function of the explosion energy, ejecta mass, and magnetar parameters. We then estimate the ULTRASAT detection horizon (z < 0.15) as a function of the same physical parameters, and the overall expected detection rate, finding that magnetar-powered SBOs may represent up to 1/5 of the total events detected by ULTRASAT. Moreover, at the expected sensitivity of the LIGO/Virgo/Kagra O5 science run, one such event occurring within 5 Mpc will provide an ideal trigger for a GW long-transient search. Future GW detectors like the Einstein Telescope will push the horizon for joint EM-GW detections to 35–40 Mpc.