We report deep radio observations of nearby Type Ia supernovae (SNe Ia) with the electronic Multi-Element Radio Linked Interferometer Network and the Australia Telescope Compact Array. No detections were made. With standard assumptions for the energy densities of relativistic electrons going into a power-law energy distribution and the magnetic field strength (ε e = ε B = 0.1), we arrive at upper limits on mass-loss rate for the progenitor system of SN 2013dy (SN 2016coj, SN 2018gv, SN 2018pv, SN 2019np) of M ≲ 12 (2.8, 1.3, 2.1, 1.7) × 10-8 M⊙yr-1( vw / 100 km s-1), where v w is the wind speed of the mass loss. To SN 2016coj, SN 2018gv, SN 2018pv, and SN 2019np we add radio data for 17 other nearby SNe Ia and model their nondetections. With the same model as described, all 21 SNe Ia have M ≲ 4 × 10-8 M⊙yr-1( vw / 100 km s-1) . We compare those limits with the expected mass-loss rates in different single-degenerate progenitor scenarios. We also discuss how information on e and B can be obtained from late observations of SNe Ia and the youngest SN Ia remnant detected in radio, G1.9+0.3, as well as stripped-envelope core-collapse SNe. We highlight SN 2011dh and argue for ε e ≈ 0.1 and ε B ≈ 0.0033. Finally, we discuss strategies to observe at radio frequencies to maximize the chance of detection, given the time since explosion, the distance to the SN, and the telescope sensitivity.