The event horizon of a black hole in general relativity absorbs all infalling radiation. Any observation of the contrary would immediately challenge the expectation that astrophysical black holes are described by the vacuum Kerr geometry. if a putative black hole does reflect part of the ingoing radiation, its quasinormal mode structure is drastically altered. Low frequency modes can be introduced that are resonantly excited during the inspiral of a binary system. We study the resulting phase shift of the gravitational wave signal. Building on neutron star results, we obtain a model-independent expression for the phase shift that depends only on quasinormal modes and Love numbers of the compact object. We find that the phase shift might be detectable with Einstein Telescope for asymmetric binaries in high signal-to-noise events (similar to 10(3)), but by far cannot explore the Planck scale.