Abstract We present the largest and deepest late-time radio and millimeter survey to date of superluminous supernovae (SLSNe) and long-duration gamma-ray bursts (LGRBs) to search for associated nonthermal synchrotron emission. Using the Karl G. Jansky Very Large Array (VLA) and the Atacama Large Millimeter/submillimeter Array (ALMA), we observed 43 sources at 6 and 100 GHz on a timescale of ∼ 1–19 yr post-explosion. We do not detect radio/millimeter emission from any of the sources, with the exception of a 6 GHz detection of PTF10hgi, as well as the detection of 6 GHz emission near the location of the SLSN PTF12dam, which we associate with its host galaxy. We use our data to place constraints on central engine emission due to magnetar wind nebulae and off-axis relativistic jets. We also explore nonrelativistic emission from the SN ejecta, and place constraints on obscured star formation in the host galaxies. In addition, we conduct a search for fast radio bursts (FRBs) from some of the sources using VLA phased-array observations; no FRBs are detected to a limit of 16 mJy (7σ; 10 ms duration) in about 40 minutes on source per event. A comparison to theoretical models suggests that continued radio monitoring may lead to detections of persistent radio emission on timescales of ≳ a decade.