  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 non-thermal 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 $\sim 1 - 19$ yr post-explosion. We do not detect radio/mm
emission from any of the sources, with the exception of a 6 GHz detection of
PTF10hgi (Eftekhari et al. 2019), 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
non-relativistic 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 ($7\sigma$; 10 ms
duration) in about 40 min 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 $\gtrsim {\rm decade}$.
