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Low-loss deposited dielectrics will benefit superconducting devices such as integrated superconducting spectrometers, superconducting qubits, and kinetic inductance parametric amplifiers. Compared with planar structures, multilayer structures such as microstrips are more compact and eliminate radiation loss at high frequencies. Multilayer structures are most easily fabricated with deposited dielectrics, which typically exhibit higher dielectric loss than crystalline dielectrics. We measure the subkelvin and low-power microwave and millimeter-submillimeter-wave dielectric loss of hydrogenated amorphous silicon carbide (a-SiC:H), using superconducting chips with Nb-Ti-N/a-SiC:H/Nb-Ti-N microstrip resonators. We deposit the a-SiC:H by plasma-enhanced chemical vapor deposition at a substrate temperature of 400°C. The a-SiC:H has a millimeter-submillimeter loss tangent ranging from 0.9×10-4 at 270 GHz to 1.5×10-4 at 385 GHz. The microwave loss tangent is 3.1×10-5. These are the lowest low-power subkelvin loss tangents that have been reported for microstrip resonators at millimeter-submillimeter and microwave frequencies. The a-SiC:H films are free of blisters and have low stress: -20 MPa compressive at 200-nm thickness to 60 MPa tensile at 1000-nm thickness., Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public., Tera-Hertz Sensing, Electronic Components, Technology and Materials