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Abstract: Effective field theory (EFT) provides a way of parameterising strong-field deviations from General Relativity that might be observable in the gravitational waves emitted in a black hole merger. To perform numerical simulations of mergers in such theories it is necessary that the equations be written in a form that admits a well-posed initial value formulation. Until now it has not been known how to do this for equations involving higher derivative EFT corrections. In this talk I will describe recent work with Aron Kovacs in which we found a well-posed formulation of the equations of motion for gravity coupled to a scalar field including the leading (4-derivative) EFT corrections. This is based on a new class of ``modified harmonic” gauges that may also have applications in conventional GR.