The lack of coherent room-temperature sources in the whole terahertz spectral window (0.3-10 THz) has significantly hampered the growth of scientific and technological applications in this range. Among them, highprecision frequency measurements of molecular transitions play a central role but remain an open challenge. Here, room-temperature generation and detection of continuous-wave, broadly tunable, narrow-linewidth THz radiation are presented, and their application to high-resolution spectroscopy in the broad 1-7.5 THz spectral range is demonstrated. This result has been achieved by implementing a Cherenkov phase-matching scheme into a channel waveguide in a nonlinear crystal. This simple approach, entirely based on robust telecom technology, unprecedently merges in a single source an ultra-broad continuous wave spectral coverage and a state-of-the-art accuracy (∼ 10 −9 ) in molecular transition center determination.