  We present results from a search for gravitational-wave bursts coincident
with a set of two core-collapse supernovae observed between 2007 and 2011. We
employ data from the Laser Interferometer Gravitational-wave Observatory
(LIGO), the Virgo gravitational-wave observatory, and the GEO 600
gravitational-wave observatory. The targeted core-collapse supernovae were
selected on the basis of (1) proximity (within approximately 15 Mpc), (2)
tightness of observational constraints on the time of core collapse that
defines the gravitational-wave search window, and (3) coincident operation of
at least two interferometers at the time of core collapse. We find no plausible
gravitational-wave candidates. We present the probability of detecting signals
from both astrophysically well-motivated and more speculative
gravitational-wave emission mechanisms as a function of distance from Earth,
and discuss the implications for the detection of gravitational waves from
core-collapse supernovae by the upgraded Advanced LIGO and Virgo detectors.
