  We have used two methods to search for surviving companions of Type Ia
supernova progenitors in three Balmer-dominated supernova remnants (SNRs) in
the Large Magellanic Cloud: 0519-69.0, 0505-67.9 (DEM L71), and 0548-70.4. In
the first method, we use the Hubble Space Telescope photometric measurements of
stars to construct color-magnitude diagrams (CMDs), and compare positions of
stars in the CMDs with those expected from theoretical post-impact evolution of
surviving main sequence or helium star companions. No obvious candidates of
surviving companion are identified in this photometric search. Future models
for surviving red giant companions or with different explosion mechanisms are
needed for thorough comparisons with these observations in order to make more
definitive conclusions. In the second method, we use Multi-Unit Spectroscopic
Explorer (MUSE) observations of 0519-69.0 and DEM L71 to carry out
spectroscopic analyses of stars in order to use large peculiar radial
velocities as diagnostics of surviving companions. We find a star in 0519-69.0
and a star in DEM L71 moving at radial velocities of 182 $\pm$ 0 km s$^{-1}$
and 213 $\pm$ 0 km s$^{-1}$, more than 2.5$\sigma$ from the mean radial
velocity of the underlying stellar population, 264 km s$^{-1}$ and 270 km
s$^{-1}$, respectively. These stars need higher-quality spectra to investigate
their abundances and rotation velocities to determine whether they are indeed
surviving companions of the SN progenitors.
