  Inspiralling compact binaries as standard sirens will soon become an
invaluable tool for cosmology when advanced interferometric gravitational-wave
detectors begin their observations in the coming years. However, a degeneracy
in the information carried by gravitational waves between the total rest-frame
mass $M$ and the redshift $z$ of the source implies that neither can be
directly extracted from the signal, but only the combination $M(1+z)$, the
redshifted mass. Recent work has shown that for binary neutron star systems, a
tidal correction to the gravitational-wave phase in the late-inspiral signal
that depends on the rest-frame source mass could be used to break the
mass-redshift degeneracy. We propose here to use the signature encoded in the
post-merger signal to deduce the redshift to the source. This will allow an
accurate extraction of the intrinsic rest-frame mass of the source, in turn
permitting the determination of source redshift and luminosity distance solely
from gravitational-wave observations. This will herald a new era in precision
cosmography and astrophysics. Using numerical simulations of binary neutron
star mergers of very slightly different mass, we model gravitational-wave
signals at different redshifts and use Bayesian parameter estimation to
determine the accuracy with which the redshift can be extracted for a source of
known mass. We find that the Einstein Telescope can determine the source
redshift to $sim 10$--$20%$ at redshifts of $z<0.04$.
