The optical emission from a pair of nanoantennas is investigated within the theoretical framework of quantum electrodynamics. The analysis of fluorescent emission from a pair of molecular antenna species in close proximity is prompted by experimental work on oriented semiconductor polymer nanostructures. Each physically different possibility for separation-dependent features in photon emission by any such pair is explored in detail, leading to the identification of three distinct mechanisms: emission from a pair-delocalized exciton state, emission that engages electrodynamic coupling through quantum interference, and correlated photon emission from the two components of the pair. Although each mechanism produces a damped oscillatory dependence on the pair separation, each of the corresponding results exhibits an analytically different form. Significant differences in the associated spatial frequencies enable an apparent ambiguity in the interpretation of experiments to be resolved. Other major differences are found in the requisite conditions, the associated selection rules, and the variation with angular disposition of the emitters, together offering grounds for experimental discrimination between the coupling mechanisms. The analysis paves the way for investigations of pair-wise coupling effects in the emission from nanoantenna arrays.