A novel Metamaterial Dipole Model (MDM) has been proposed as a powerful tool for modeling and designing metasurface antennas for numerous applications such as beamforming arrays, holograms, and flat lenses among others. In this technique, a metasurface antenna is described as a collection of effective magnetic dipoles characterized by their polarizability. The utility of this modeling technique relies on polarizability extraction, i.e.The proper characterization of each individual metamaterial element when it is embedded in a waveguide. In this presentation, we employ a volumetric equivalence principle in a comprehensive procedure for retrieving the polarizability of complementary metamaterial elements, when these are embedded in rectangular waveguides, planar waveguides, and periodic metascreens. We demonstrate that the extracted polarizability changes for each supporting waveguide structure, highlighting the importance of proper characterization of metamaterial elements in different environments.