  Gravitational waves emitted by chirping supermassive black hole binaries
could in principle be used to obtain very accurate distance determinations.
Provided they have an electromagnetic counterpart from which the redshift can
be determined, these standard sirens could be used to build a high redshift
Hubble diagram. Errors in the distance measurements will most likely be
dominated by gravitational lensing. We show that the (de)magnification due to
inhomogeneous foreground matter will increase the scatter in the measured
distances by a factor ~10. We propose to use optical and IR data of the
foreground galaxies to minimize the degradation from weak lensing. We find that
the net effect of correcting the estimated distances for lensing is comparable
to increasing the sample size by a factor of three when using the data to
constrain cosmological parameters.
