The metallo-$eta$-lactamases ($M{eta}Ls$) are clinically significant enzymes which readily hydrolyze most $eta$-lactam antibiotics. Discovering potential inhibitors for the $M{eta}Ls$ is an expensive, time consuming endeavor. Virtual screening can sieve out inhibitor candidates with incompatible features prior to synthesis, decreasing these costs. Using Autodock 4.0, the binding locations and energies of four previously-studied potential inhibitors and four additional compounds obtained from the National Cancer Institute (NCI) database were computationally calculated. Based on the docking models of these eight compounds, we then designed several hypothetical inhibitor structures, compounds A through F, and performed their respective docking experiments. The docking results for compound F showed that it binds to the zinc containing active sites with a lowest predicted binding energy of -6.70 kcal/mol, suggesting F is the most likely potential $M{eta}L$ inhibitor.