Mutations in the epitopes of antigenic proteins can confer viral resistance to antibody-mediated neutralization. However, the fundamental properties that characterize epitope residues and how mutations affect antibody binding to alter virus susceptibility to neutralization remain largely unknown. To address these questions, we used an ensemble-based algorithm to characterize the effects of mutations on the thermodynamics of protein conformational fluctuations. We applied this method to the envelope protein domain III (ED3) of two medically important flaviviruses: West Nile and dengue 2. We determined an intimate relationship between the susceptibility of a residue to thermodynamic perturbations and epitope location. This relationship allows the successful identification of the primary epitopes in each ED3, despite their high sequence and structural similarity. Mutations that allow the ED3 to evade detection by the antibody either increase or decrease conformational fluctuations of the epitopes through local effects or long-range interactions. Spatially distant interactions originate in the redistribution of conformations of the ED3 ensembles, not through a mechanically connected array of contiguous amino acids. These results reconcile previous observations of evasion of neutralization by mutations at a distance from the epitopes. Finally, we established a quantitative correlation between subtle changes in the conformational fluctuations of the epitope and large defects in antibody binding affinity. This correlation suggests that mutations that allow viral growth, while reducing neutralization, do not generate significant structural changes and underscores the importance of protein fluctuations and long-range interactions in the mechanism of antibody-mediated neutralization resistance.