Evanescent Floquet modes (EFMs) are boundary-free solutions of a half-space, that is stationary quasi-bulk states. These states build a complete solution basis of slab-like geometries and thus help us understand scattering behavior at and quantum emission in metamaterials. With no out-of-the-box solution available to calculate EFMs, the aim of this project is to develop the necessary algoritmic tools. Our strategy is two-fold: on the one hand, to efficiently compute EFMs and extract their meaning, we use a combined Greens Galerkin procedure and approximate the fields in one sub-domain (generally metallic) of binary metamaterials using a small number of polynomial basis functions. On the other hand, we employ commercial software and solve the associated non-linear holomorphic eigenproblem with a Newton method. While the first approach is computationally relatively cheap and yields additional physical insight, the second approach is more versatile and produces reliable results to benchmark the former.