The response of a semi-infinite ocean to a slowly travelling atmospheric perturbation crossing the coast provides a simple example of the breakdown of nearly geostrophic balance induced by a boundary. We examine this response in the linear shallow-water model at small Rossby number$\varepsilon \ll 1$. Using matched asymptotics, we show that a long Kelvin wave, with$O(\varepsilon ^{-1})$length scale and$O(\varepsilon )$amplitude relative to quasi-geostrophic response, is generated as the perturbation crosses the coast. Accounting for this Kelvin wave restores the conservation of mass that is violated in the quasi-geostrophic approximation.