  We present a detailed description of techniques developed to combine 3D
numerical simulations and, subsequently, a single black hole close-limit
approximation. This method has made it possible to compute the first complete
waveforms covering the post-orbital dynamics of a binary black hole system with
the numerical simulation covering the essential non-linear interaction before
the close limit becomes applicable for the late time dynamics. To determine
when close-limit perturbation theory is applicable we apply a combination of
invariant a priori estimates and a posteriori consistency checks of the
robustness of our results against exchange of linear and non-linear treatments
near the interface. Once the numerically modeled binary system reaches a regime
that can be treated as perturbations of the Kerr spacetime, we must
approximately relate the numerical coordinates to the perturbative background
coordinates. We also perform a rotation of a numerically defined tetrad to
asymptotically reproduce the tetrad required in the perturbative treatment. We
can then produce numerical Cauchy data for the close-limit evolution in the
form of the Weyl scalar $\psi_4$ and its time derivative $\partial_t\psi_4$
with both objects being first order coordinate and tetrad invariant. The
Teukolsky equation in Boyer-Lindquist coordinates is adopted to further
continue the evolution. To illustrate the application of these techniques we
evolve a single Kerr hole and compute the spurious radiation as a measure of
the error of the whole procedure. We also briefly discuss the extension of the
project to make use of improved full numerical evolutions and outline the
approach to a full understanding of astrophysical black hole binary systems
which we can now pursue.
