Jointed interfaces, damage, wear, or non-idealized boundary conditions often introduce nonlinear characteristics to assembled structures. Consequently, extensive research has been carried out regarding nonlinear system identification. The development of nonlinear system identification is also enabling the intentional application of nonlinearities towards practical fields such as vibration control and energy harvesting. This research proposes a nonlinear identification procedure that consists of two steps: first, the raw data is filtered by the Double Reverse Multimodal Decomposition method that involves system reconstruction, expansion, and filtering twice. Second, the Peak Finding and Fitting method is applied to the filtered signal to extract the instantaneous amplitude and frequency. The identification procedure is applied to the measured responses from a jointed structure to assess its efficacy. The results are compared with those obtained from other well-known methods—the Hilbert transform and zero-crossing methods. The comparison results indicate that the Peaking Finding and Fitting method extracts the amplitude of the response signal more accurately. Consequently, this yields a higher signal-to-noise ratio in the extracted damping values. As a recommended last step, uncertainty assessment is conducted to calculate the 95% confidence intervals of the nonlinear properties of the system.