The identification of protein mutations that enhance binding affinity may be achieved by computational or experimental means, or by a combination of the two. Sources of affinity enhancement may include improvements to the net balance of binding interactions of residues forming intermolecular contacts at the binding interface, such as packing and hydrogen-bonding interactions. Here we identify noncontacting residues that make substantial contributions to binding affinity and that also provide opportunities for mutations that increase binding affinity of the TEM1 beta-lactamase (TEM1) to the beta-lactamase inhibitor protein (BLIP). A region of BLIP not on the direct TEM1-binding surface was identified for which changes in net charge result in particularly large increases in computed binding affinity. Some mutations to the region have previously been characterized, and our results are in good correspondence with this results of that study. In addition, we propose novel mutations to BLIP that were computed to improve binding significantly without contacting TEM1 directly. This class of noncontacting electrostatic interactions could have general utility in the design and tuning of binding interactions.