  Young supernova remnants (SNRs) provide a unique perspective on supernova
(SN) progenitors and connect the late evolution of SNe with the onset of the
SNR phase. Here we study SN 1885A and G1.9+0.3, the most recent thermonuclear
SNe in the Local Group (with ages $\sim 100$ years) with radio data, which
provides a sensitive probe of the SN environment and energetics. We reduce and
co-add 4-8 GHz observations from Karl G. Jansky Very Large Array (VLA) to
produce the deepest radio image of the M31 central region (RMS noise of 1.3
$\mu$Jy/beam at 6.2 GHz). We detect some diffuse emission near SN 1885A at 2.6
$\sigma$, but the association with SN 1885A is uncertain because diffuse radio
emission pervades the M31 central region. The VLA upper limit and HST
measurements yield an ambient density, $n_0 < 0.04$ cm$^{-3}$ ($\pm$ 0.03
cm$^{-3}$ due to systematics) for SN 1885A, and kinetic energies, $E_k \sim
(1.3-1.7) \times 10^{51}$ ergs for ejecta masses of $1-1.4$ M$_{\odot}$. For
the same ejecta mass range, VLA observations of G1.9+0.3 yield $n_0 = 0.18$
cm$^{-3}$, and $E_k = (1-1.3) \times 10^{51}$ ergs. We argue that a
sub-Chandrasekhar explosion model may be likely for SN 1885A, in agreement with
X-ray studies, but in tension with models for the HST absorption spectra. The
analysis of G1.9+0.3 is consistent with both Chandrasekhar and
sub-Chandrasekhar SN Ia models, but rules out Type Iax explosions.
