  Randomized Benchmarking allows to efficiently and scalably characterize the
average error of an unitary 2-design such as the Clifford group $\mathcal{C}$
on a physical candidate for quantum computation, as long as there are no
non-computational leakage levels in the system. We investigate the effect of
leakage errors on Randomized Benchmarking induced from an additional level per
physical qubit and provide a modified protocol that allows to derive reliable
estimates for the error per gate in their presence. We assess the variance of
the sequence fidelity corresponding to the number of random sequences needed
for valid fidelity estimation. Our protocol allows for gate dependent error
channels without being restricted to perturbations. We show that our protocol
is compatible with Interleaved Randomized Benchmarking and expand to
benchmarking of arbitrary gates. This setting is relevant for superconducting
transmon qubits, among other systems.
