Honeycomb composites are common materials in applications where a high specific stiffness is required. Previous research has found that honeycombs with polymer infills in their cells exhibit effective stiffnesses greater than the honeycomb or polymer alone. Currently, the state of analytic models for predicting the effective properties of these honeycomb polymer composites is limited, thus further research is needed to better characterize the behavior of these materials. In this work, a nonlinear finite element analysis was employed to perform parametric studies of a filled honeycomb unit cell with isotropic wall and infill materials. A pinned rigid wall model was created as an upper bound on the deformable wall model’s performance, and an empty honeycomb model was employed to better understand the mechanisms of stiffness amplification. Mechanisms by which the stiffness amplification occurs is studied through parametric studies, and the results are compared to current analytic models. It has been observed that both the volume change within the honeycomb cell under deformation, and the mismatch in Poisson’s ratios between the honeycomb and infill influence the effective properties. Stiffness amplifications of over 4,000 have been observed, with auxetic behavior achieved by tailoring of the HPC geometry. This research provides an important step toward understanding the design space and benefits of honeycomb polymer composites, and demonstrates the possibilities for variable stiffness structures when considering smart material infill materials.