  The accurate modeling of gravitational radiation is a key issue for
gravitational wave astronomy. As simulation codes reach higher accuracy,
systematic errors inherent in current numerical relativity wave-extraction
methods become evident, and may lead to a wrong astrophysical interpretation of
the data. In this paper, we give a detailed description of the
Cauchy-characteristic extraction technique applied to binary black hole
inspiral and merger evolutions to obtain gravitational waveforms that are
defined unambiguously, that is, at future null infinity. By this method we
remove finite-radius approximations and the need to extrapolate data from the
near zone. Further, we demonstrate that the method is free of gauge effects and
thus is affected only by numerical error. Various consistency checks reveal
that energy and angular momentum are conserved to high precision and agree very
well with extrapolated data. In addition, we revisit the computation of the
gravitational recoil and find that finite radius extrapolation very well
approximates the result at $\scri$. However, the (non-convergent) systematic
differences to extrapolated data are of the same order of magnitude as the
(convergent) discretisation error of the Cauchy evolution hence highlighting
the need for correct wave-extraction.
