Predicting protein interaction specificity from sequence is an important goal in computational biology. We present a model for predicting the interaction preferences of coiled-coil peptides derived from bZIP transcription factors that performs very well when tested against experimental protein microarray data. We used only sequence information to build atomic-resolution structures for 1711 dimeric complexes, and evaluated these with a variety of functions based on physics, learned empirical weights or experimental coupling energies. A purely physical model, similar to those used for protein design studies, gave reasonable performance. The results were improved significantly when helix propensities were used in place of a structurally explicit model to represent the unfolded reference state. Further improvement resulted upon accounting for residue-residue interactions in competing states in a generic way. Purely physical structure-based methods had difficulty capturing core interactions accurately, especially those involving polar residues such as asparagine. When these terms were replaced with weights from a machine-learning approach, the resulting model was able to correctly order the stabilities of over 6000 pairs of complexes with greater than 90% accuracy. The final model is physically interpretable, and suggests specific pairs of residues that are important for bZIP interaction specificity. Our results illustrate the power and potential of structural modeling as a method for predicting protein interactions and highlight obstacles that must be overcome to reach quantitative accuracy using a de novo approach. Our method shows unprecedented performance in predicting protein-protein interaction specificity accurately using structural modeling and suggests that predicting coiled-coil interactions generally may be within reach.