  Structure at the horizon scale of black holes would give rise to echoes of
the gravitational wave signal associated with the post-merger ringdown phase in
binary coalescences. We study the waveform of echoes in static and stationary,
traversable wormholes in which perturbations are governed by a symmetric
effective potential. We argue that echoes are dominated by the wormhole
quasinormal frequency nearest to the fundamental black hole frequency that
controls the primary signal. We put forward an accurate method to construct the
echoes waveform(s) from the primary signal and the quasinormal frequencies of
the wormhole, which we characterize. We illustrate this in the static
Damour-Solodukhin wormhole and in a new, rotating generalization that
approximates a Kerr black hole outside the throat. Rotation gives rise to a
potential with an intermediate plateau region that breaks the degeneracy of the
quasinormal frequencies. Rotation also leads to late-time instabilities which,
however, fade away for small angular momentum.
