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We predict superconductivity for the carbon–boron clathrate SrB_{3}C_{3} with T_{c}=27–43K 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 (>3000K 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 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.