  Space-born gravitational-wave interferometers such as {\it LISA} will detect
the gravitational wave (GW) signal from the inspiral, plunge and ringdown
phases of massive black hole binary mergers at cosmological distances. From the
inspiral waves, we will be able to measure the masses of the binaries' members;
from the ringdown waves, we will be able to measure the mass of the final
merged remnant. A subset of detected events allow the identification of both
the inspiral and the ringdown waveforms in a given source, and thus allow a
measurement of the total mass-energy lost to GWs over the coalescence, $M_{\rm
GW}$. We define ``golden'' binary mergers to be those with measurement errors
likely to be small enough for a physically useful determination of $M_{\rm
GW}$. A detailed sensitivity study, combined with simple black hole population
models, suggests that a few golden binary mergers may be detected during a
3-year {\it LISA} mission lifetime. Any such mass deficit measurement would
constitute a robust and valuable observational test of strong-field
relativistic gravity. An extension of this concept to include spin measurements
may allow a direct empirical test of the black hole area theorem.
