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 us 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.