  Coherent superposition is a key feature of quantum mechanics that underlies
the advantage of quantum technologies over their classical counterparts.
Recently, coherence has been recast as a resource theory in an attempt to
identify and quantify it in an operationally well-defined manner. Here we study
how the coherence present in a state can be used to implement a quantum channel
via incoherent operations and, in turn, to assess its degree of coherence. We
introduce the robustness of coherence of a quantum channel---which reduces to
the homonymous measure for states when computed on constant-output
channels---and prove that: i) it quantifies the minimal rank of a maximally
coherent state required to implement the channel; ii) its logarithm quantifies
the amortized cost of implementing the channel provided some coherence is
recovered at the output; iii) its logarithm also quantifies the zero-error
asymptotic cost of implementation of many independent copies of a channel. We
also consider the generalized problem of imperfect implementation with
arbitrary resource states. Using the robustness of coherence, we find that in
general a quantum channel can be implemented without employing a maximally
coherent resource state. In fact, we prove that \textit{every} pure coherent
state in dimension larger than $2$, however weakly so, turns out to be a
valuable resource to implement \textit{some} coherent unitary channel. We
illustrate our findings for the case of single-qubit unitary channels.
