It remains a challenge to generate coherent radiation in the spectral range of 0.1-10 THz (“the THz gap”), a band for applications ranging from spectroscopy to security and high-speed wireless communications. Here, we disclose how to produce coherent radiation spanning the THz gap using efficient second-harmonic generation (SHG) in low-loss dielectric structures, starting from an electronic oscillator (EO) that generates coherent radiation at frequencies of about 100 GHz. The EO is coupled to cascaded, hybrid THz-band dielectric cavities that combine (1) extreme field concentration in high-quality-factor resonators with (2) nonlinear materials enhanced by phonon resonances. These cavities convert the input radiation into higher-frequency coherent radiation at conversion efficiencies of >103%/W, making it possible to bridge the THz gap with 1 W of input power. This approach enables efficient, cascaded parametric frequency converters, representing a new generation of light sources extensible into the mid-IR spectrum and beyond.