We present a search for late-time rebrightening of radio emission from three supernovae (SNe) with associated gamma-ray bursts (GRBs). It has been previously proposed that the unusually energetic SNe associated with GRBs should enter the Sedov-Taylor phase decades after the stellar explosion, and this SN "remnant" emission will outshine the GRB radio afterglow and be detectable at significant distances. We place deep limits on the radio luminosity of GRB 980425/SN 1998bw, GRB 030329/SN 2003dh, and GRB 060218/SN 2006aj, 10-18 yr after explosion, with our deepest limit being L < 4 × 1026 erg s−1 Hz−1 for GRB 980425/SN 1998bw. We put constraints on the density of the surrounding medium for various assumed values of the microphysical parameters related to the magnetic field and synchrotron-emitting electrons. For GRB 060218/SN 2006aj and GRB 980425/SN 1998bw, these density limits have implications for the density profile of the surrounding medium, while the nondetection of GRB 030329/SN 2003dh implies that its afterglow will not be detectable anymore at gigahertz frequencies.