document: Although the free Kelvin wave problem is of considerable theoretical importance, problems with forcing and damping have greater practical importance. In nature, the forcing could be due to a wind stress at the free surface or an astronomical tidal potential, and the damping could be due to the turbulent stress of a bottom boundary layer. Regardless of the details, the forced response is composed of shallow-water waves, possibly including Kelvin waves, with the largest amplitudes in waves with a natural frequency ωf close to that of the forcing frequency ω; various examples of this sort are given in Chapters 9 and 10 of Gill [16]. When ω≈ωf, there is a large amplitude near-resonant response, the size of which is sensitive to the weak damping and |ω−ωf|. Thus, in numerical solutions of near-resonantly forced waves, we anticipate that errors in ωf (associated with the spatial discretisation) could lead to non-trivial errors in the forced response.