This work presents a new method for creating gravitational waveform templates for black hole binaries with an intermediate mass-ratio. Intermediate-mass-ratio inspirals (IMRIs) are currently an open problem in gravitational-wave source modelling. While black hole perturbation theory can accurately model extreme-mass-ratio inspirals, and numerical relativity has seen much success modelling comparable-mass inspirals, neither approach currently works well on its own for IMRIs. It is not clear how adequate a purely perturbative treatment can be at intermediate mass-ratios of 1:100-1:1000, and at such mass ratios the length-scale disparity remains large enough to pose a serious challenge for numerical relativity.Here we work to provide accurate modelling of such binaries through a synergistic combination of black-hole perturbation and numerical relativity techniques. Our approach matches an approximate analytical solution near the smaller black hole (formed from the tidally perturbed black hole metric) to a fully nonlinear numerical solution in the bulk of the spacetime. This has the effect of relieving some of the scale disparity.This thesis presents the details of this worldtube excision model and goes on to develop and test the architecture using a simple toy model of a scalar charge in orbit around a Schwarzschild black hole. We then present results from numerical implementations of such a test setup in 1+1D, as well as in 3+1D. Finally, we detail the model’s infrastructure in the full binary black hole case. The theoretical foundations of the model are erected, which includes the derivation of a suitable approximate analytical solution.