Coronal mass ejections (CMEs) may dramatically impact habitability and atmospheric composition of planets around magnetically active stars, including young solar analogs and many M dwarfs. Theoretical predictions of such effects are limited by the lack of observations of stellar CMEs. This thesis addresses this gap through a search for the spectral and spatial radio signatures of CMEs on active M dwarfs. Solar CMEs produce radio bursts with a distinctive spectral signature, narrow-band plasma emission that drifts to lower frequency as a CME expands outward. To search for analogous events on nearby stars, I worked on system design, software, and commissioning for the Starburst project, a wideband single-baseline radio interferometry backend dedicated to stellar observations. In addition, I led a survey of nearby active M dwarfs with the Karl G. Jansky Very Large Array (VLA), detecting coherent radio bursts in 13 out of 23 epochs, over a total of 58 hours. This survey's ultra-wide bandwidth (0.23-6.0 GHz) dynamic spectroscopy, unprecedented for stellar observations, revealed diverse behavior in the time-frequency plane. Flare star UV Ceti produced complex, luminous events reminiscent of brown dwarf aurorae; AD Leo sustained long-duration, intense, narrow-band "storms"; and YZ CMi emitted a burst with substructure with rapid frequency drift, resembling solar Type III bursts, which are attributed to electrons moving at speeds of order 10% of the speed of light. To search for the spatial signature of CMEs, I led 8.5-GHz observations with the Very Long Baseline Array simultaneous to 24 hours of the VLA survey. This program detected non-thermal continuum emission from the stars in all epochs, as well as continuum flares on AD Leo and coherent bursts on UV Ceti, enabling measurement of the spatial offset between flaring and quiescent emission. These observations demonstrate the diversity of stellar transients that can be expected in time-domain radio surveys, especially with the advent of large low-frequency radio telescopes. Wide bandwidth radio dynamic spectroscopy, complemented by high-resolution imaging of the radio corona, is a powerful technique for detecting stellar eruptions and characterizing dynamic processes in the stellar corona.