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Frequency estimation of undersampled waveforms receives increasing attention in communication, radar signal processing, instrumentation and measurements, and so on. However, due to the lack of recognizing the correct remainder between two side spectra, the existing Chinese Remainder Theorem (CRT)-based frequency estimators can hardly deal with real-valued signals. To achieve this goal, this paper proposes an estimator combining spectrum correction (aiming to enhance reconstruction accuracy by incorporating the fractional parts of DFT remainders), closed-form CRT, and a remainder sifting approach. Based on the detection of an undersampled waveform's zero crossing point, this solution can pick out the correct remainder between two side spectra, which ensures that the CRT achieves a valid reconstruction. Compared with the existing Maroosi-Bizaki estimator, the proposed method not only enlarges the upper bound of frequency recovery but also possesses higher reconstruction accuracy (the relative error is less than 0.002%) with lower consumption of computational complexity. The numerical results verify the superior performances of our estimator.