  Many simulations of gravitational collapse to black holes become inaccurate
before the total emitted gravitational radiation can be determined. The main
difficulty is that a significant component of the radiation is still in the
near-zone, strong field region at the time the simulation breaks down. We show
how to calculate the emitted waveform by matching the numerical simulation to a
perturbation solution when the final state of the system approaches a
Schwarzschild black hole. We apply the technique to two scenarios: the head-on
collision of two black holes, and the collapse of a disk to a black hole. This
is the first reasonably accurate calculation of the radiation generated from
colliding black holes that form from matter collapse.
