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Ternary quantum processors offer significant computational advantages over conventional qubit technologies, leveraging the encoding and processing of quantum information in qutrits (three-level systems). To evaluate and compare the performance of such emerging quantum hardware it is essential to have robust benchmarking methods suitable for a higher-dimensional Hilbert space. We demonstrate extensions of industry standard Randomized Benchmarking (RB) protocols, developed and used extensively for qubits, suitable for ternary quantum logic. Using a superconducting five-qutrit processor, we find a single-qutrit gate infidelity as low as $2.38 \times 10^{-3}$. Through interleaved RB, we find that this qutrit gate error is largely limited by the native (qubit-like) gate fidelity, and employ simultaneous RB to fully characterize cross-talk errors. Finally, we apply cycle benchmarking to a two-qutrit CSUM gate and obtain a two-qutrit process fidelity of $0.82$. Our results demonstrate a RB-based tool to characterize the obtain overall performance of a qutrit processor, and a general approach to diagnose control errors in future qudit hardware.