  Several quantum-gravity models of compact objects predict microscopic or even
Planckian corrections at the horizon scale. We explore the possibility of
measuring two model-independent, smoking-gun effects of these corrections in
the gravitational waveform of a compact binary, namely the absence of tidal
heating and the presence of tidal deformability. For events detectable by the
future space-based interferometer LISA, we show that the effect of tidal
heating dominates and allows one to constrain putative corrections down to the
Planck scale. The measurement of the tidal Love numbers with LISA is more
challenging but, in optimistic scenarios, it allows to constrain the
compactness of a supermassive exotic compact object down to the Planck scale.
Our analysis suggests that highly-spinning, supermassive binaries at 1-20 Gpc
provide unparalleled tests of quantum-gravity effects at the horizon scale.
