  Recent observations support the hypothesis that a large fraction of
"short-hard" gamma-ray bursts (SHBs) are associated with compact binary
inspiral. Since gravitational-wave (GW) measurements of well-localized
inspiraling binaries can measure absolute source distances, simultaneous
observation of a binary's GWs and SHB would allow us to independently determine
both its luminosity distance and redshift. Such a "standard siren" (the GW
analog of a standard candle) would provide an excellent probe of the relatively
nearby universe's expansion, complementing other standard candles. In this
paper, we examine binary measurement using a Markov Chain Monte Carlo technique
to build the probability distributions describing measured parameters. We
assume that each SHB observation gives both sky position and the time of
coalescence, and we take both binary neutron stars and black hole-neutron star
coalescences as plausible SHB progenitors. We examine how well parameters
particularly distance) can be measured from GW observations of SHBs by a range
of ground-based detector networks. We find that earlier estimates overstate how
well distances can be measured, even at fairly large signal-to-noise ratio. The
fundamental limitation to determining distance proves to be a degeneracy
between distance and source inclination. Overcoming this limitation requires
that we either break this degeneracy, or measure enough sources to broadly
sample the inclination distribution. (Abridged)
