Additive Manufacturing (AM) techniques allow the production of complex geometries unattainable through other traditional technologies. This advantage lends itself well to rapidly iterating and improving upon the design of microwave photonic crystals, which are structures with intricate, repeating features. The issue tackled by this work involves compounding a high-permittivity material that can be used to produce 3D microwave photonic structures using polymer extrusion-based AM techniques. This material was acrylonitrile butadiene styrene (ABS)-based and used barium titanate (BaTiO3) ceramic as the high-permittivity component of the composite and involved the use of a surfactant and a plasticizer to facilitate processing. Initial small amounts of the material were compounded using an internal batch mixer and studied using polymer thermal analysis techniques, such as thermogravimetric analysis, rheometry, and differential scanning calorimetry to determine the proper processing conditions. The production of the material was then scaled up using a twin-screw extruder system, producing homogeneous pellets. Finally, the thermoplastic composite was used with a screw-based, material extrusion additive manufacturing technique to produce a slab for measuring the relative permittivity of the material, as well as a preliminary 3D photonic crystal. The real part of the permittivity was measured to be 12.85 (loss tangent = 0.046) in the range of 10 to 12 GHz, representing the highest permittivity ever demonstrated for a thermoplastic AM composite at microwave frequencies.