We derive thermodynamically an expression for the theoretical open circuit voltage of a rectenna device that converts high frequency ac radiation into dc power output. In addition, we obtain the conversion efficiency of an electron emission rectenna, which consists of a nano-antenna collector and a geometrically asymmetric rectifying MVM tunnel junction. This quantity plays an analogous role to the fill factor for conventional n–p semiconducting PV devices in limiting the overall efficiency. Thus, in effect, we develop a theory analogous to the Shockley–Queisser theory or limit (SHQL) for rectennas. The predicted limitations on the efficiency of the electron emission device, as in the case of the SHQL for n–p junction devices, are useful for guiding the development of practical devices based on rectennas[1]. These are useful benchmarks for evaluating different electron emission-based schemes for energy conversion.