  Microwave cavity resonators are crucial components of many quantum
technologies and are a promising platform for hybrid quantum systems, as their
open architecture enables the integration of multiple subsystems inside the
cavity volume. To support these subsystems within the cavity, auxiliary
structures are often required, but the effects of these structures on the
microwave cavity mode are difficult to predict due to a lack of a priori
knowledge of the materials' response in the microwave regime. Understanding
these effects becomes even more important when frequency matching is critical
and tuning is limited, for example, when matching microwave modes to atomic
resonances. Here, we study the microwave cavity mode in the presence of three
commonly-used machinable polymers, paying particular attention to the change in
resonance and the dissipation of energy. We demonstrate how to use the derived
dielectric coefficient and loss tangent parameters for cavity design in a test
case, wherein we match a polymer-filled 3D microwave cavity to a hyperfine
transition in rubidium.
