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. . These are useful benchmarks for evaluating different electron emission-based schemes for energy conversion.