A novel rectifying circuit topology is proposed for converting electromagnetic pulse waves (PWs), that are collected by a wideband antenna, into dc voltage. The typical incident signal considered in this paper consists of 10-ns pulses modulated around 2.4 GHz with a repetition period of 100 ns. The proposed rectifying circuit topology comprises a double-current architecture with inductances that collect the energy during the pulse delivery as well as an output capacitance that maintains the dc output voltage between the pulses. Experimental results show that the efficiency of the rectifier reaches 64% for a mean available incident power of 4 dBm. Similar performances are achieved when a wideband antenna is combined with the rectifier in order to realize a rectenna. By increasing the repetition period of the incident PWs to 400 ns, the rectifier still operates with an efficiency of 52% for a mean available incident pulse power of -8 dBm. Finally, the proposed PW rectenna is tested for a wireless energy transmission application in a low-Q cavity. The time reversal technique is applied to focus PWs around the desired rectenna. Results show that the rectenna is still efficient when noisy PW is handled.