The optimization of antibodies is a desirable goal towards the development of better therapeutic strategies. The antibody 11K2 was previously developed as a therapeutic tool for inflammatory diseases, and displays very high affinity (4.6 pM) for its antigen the chemokine MCP-1 (monocyte chemo-attractant protein-1). We have employed a virtual library of mutations of 11K2 to identify antibody variants of potentially higher affinity, and to establish benchmarks in the engineering of a mature therapeutic antibody. The most promising candidates identified in the virtual screening were examined by surface plasmon resonance to validate the computational predictions, and to characterize their binding affinity and key thermodynamic properties in detail. Only mutations in the light-chain of the antibody are effective at enhancing its affinity for the antigen in vitro, suggesting that the interaction surface of the heavy-chain (dominated by the hot-spot residue Phe101) is not amenable to optimization. The single-mutation with the highest affinity is L-N31R (4.6-fold higher affinity than wild-type antibody). Importantly, all the single-mutations showing increase affinity incorporate a charged residue (Arg, Asp, or Glu). The characterization of the relevant thermodynamic parameters clarifies the energetic mechanism. Essentially, the formation of new electrostatic interactions early in the binding reaction coordinate (transition state or earlier) benefits the durability of the antibody-antigen complex. The combination of in silico calculations and thermodynamic analysis is an effective strategy to improve the affinity of a matured therapeutic antibody.