The Swift-Hohenberg equation, originally derived to model convective instabilities, serves as a useful model for pattern formation. Using a formal multiple scales expansion, we can derive an amplitude equation, known as the complex Ginzburg-Landau (CGL) equation, for an anisotropic Swift-Hohenberg (aSH) equation. Solutions to (CGL) can be used to approximate solutions to (aSH) on a larger domain, with arbitrarily small residual estimates. In this talk, we will demonstrate such estimates for an approximation in the space of bounded continuous functions on R^2. We will then define uniformly local Sobolev spaces and establish similar estimates in these more suitable spaces.