We predict superconductivity for the carbon--boron clathrate ${\mathrm{SrB}}_{3}{\mathrm{C}}_{3}$ with ${T}_{c}=27\text{--}43\phantom{\rule{0.28em}{0ex}}\mathrm{K}$ for Coulomb pseudopotential (μ ^∗)values between 0.17 and 0.10 using first-principles calculations with conventional electron--phonon coupling. Electrical transport measurements, facilitated by an in situ experimental design compatible with extreme synthesis conditions ($>3000\phantom{\rule{0.28em}{0ex}}\mathrm{K}$ at 50 GPa), show nonhysteretic resistivity drops that track the calculated magnitude and pressure dependence of superconductivity for μ ^∗ ≈ 0.15, and transport measurements collected under applied magnetic fields indicate superconductivity with an onset ${T}_{c}$ of approximately 20 K at 40 GPa. Carbon-based clathrates thus represent a class of superconductors similar to other covalent metals like ${\mathrm{MgB}}_{2}$ and doped fullerenes. Carbon clathrates share structures similar to superconducting superhydrides with wide potential for tunable properties, and covalent C--B bonds allow metastable persistence at ambient conditions.