This paper addresses design and implementation of integrated rectifier-antennas (rectennas) for wireless powering at low incident power densities, from 25 to 200 μW/cm2. Source-pull nonlinear measurement of the rectifying devices is compared to harmonic-balance simulations. Optimal diode RF and dc impedances for most efficient rectification, as a function of input power, are obtained. This allows optimized antenna design, which can eliminate or simplify matching networks and improve overall efficiency. As an example of the design methodology, Schottky diodes were characterized at 1.96 GHz and an antenna is matched to the optimal complex impedance for the most efficient rectifier. For incident power density range of interest, the optimal impedance is 137 + j149 Ω, with an RF to dc conversion efficiency of the rectifying circuit alone of 63% and total rectenna efficiency of 54%.