This paper introduces a novel circuit identification method based on “fingerprints” of periodic circuit activity that does not rely on any circuit-specific reference measurements. We capture these “fingerprints”, consisting of fifty harmonics of the circuit activity, using digital circuit simulations and near-field measurements of the EM backscattering side-channel. Utilizing a novel technique and algorithm, we augment our measurements, removing sources of noise and other irregularities not present in the simulation, in order to relate an unknown circuit measurement with a known circuit simulation. A matching threshold of less than 1 dB difference between the simulated and measured fingerprints is set, and the matching performance is evaluated across multiple hardware instances exhibiting a strong resistance to false positives. Using various match statistics, decisions on the circuit identity can be made based on the simulated and measured fingerprint pair with the best matching performance. The results show that we can identify fingerprints of digital circuits with up to 95% accuracy using the proposed method.