A recently proposed oxidative damage protection mechanism in proteins relies on hole hopping escape routes formed by redox-active amino acids. We present a computational tool to identify the dominant charge hopping pathways through these residues based on the mean residence times of the transferring charge along these hopping pathways. The residence times are estimated by combining a kinetic model with well-known rate expressions for the charge-transfer steps in the pathways. We identify the most rapid hole hopping escape routes in cytochrome P450 monooxygenase, cytochrome c peroxidase, and benzylsuccinate synthase (BSS). This theoretical analysis supports the existence of hole hopping chains as a mechanism capable of providing hole escape from protein catalytic sites on biologically relevant timescales. Furthermore, we find that pathways involving the [4Fe4S] cluster as the terminal hole acceptor in BSS are accessible on the millisecond timescale, suggesting a potential protective role of redox-active cofactors for preventing protein oxidative damage.