Antibodies are used extensively in diagnostics and as therapeutic agents. Achieving high-affinity binding is important for expanding detection limits, extending dissociation half-times, decreasing drug dosages and increasing drug efficacy. However, antibody-affinity maturation in vivo often fails to produce antibody drugs of the targeted potency, making further affinity maturation in vitro by directed evolution or computational design necessary. Here we present an iterative computational design procedure that focuses on electrostatic binding contributions and single mutants. By combining multiple designed mutations, a tenfold affinity improvement to 52 pM was engineered into the anti-epidermal growth factor receptor drug cetuximab (Erbitux), and a 140-fold improvement in affinity to 30 pM was obtained for the anti-lysozyme model antibody D44.1. The generality of the methods was further demonstrated through identification of known affinity-enhancing mutations in the therapeutic antibody bevacizumab (Avastin) and the model anti-fluorescein antibody 4-4-20. These results demonstrate computational capabilities for enhancing and accelerating the development of protein reagents and therapeutics.