The Distance Constraint Model (DCM) is an ensemble-based biophysical model that integrates thermodynamic and mechanical viewpoints of protein structure. The DCM outputs a large number of structural characterizations that collectively allow for Quantified Stability-Flexibility Relationships (QSFR) to be identified and compared across protein families. Using five metallo-β-lactamases (MBLs) as a representative set, we demonstrate how QSFR properties are both conserved and varied across protein families. Similar to our characterizations on other protein families, the backbone flexibility of the five MBLs are overall visually conserved, yet there are interesting specific quantitative differences. For example, the plasmid-encoded NDM-1 enzyme, which leads to a fast spreading drug-resistant version of Klebsiella pneumoniae, has several regions of significantly increased rigidity relative to the other four. In addition, the set of intramolecular couplings within NDM-1 are also atypical. While long-range couplings frequently vary significantly across protein families, NDM-1 is distinct because it has limited correlated flexibility, which is isolated within the active site S3/S4 and S11/H6 loops. These loops are flexibly correlated in the other members, suggesting it is important to function, but the others also have significant amounts of correlated flexibility throughout the rest of their structures.