  Gravitational waves (GWs) from presumed binary black hole mergers are now
being detected on a regular basis with the Advanced LIGO and Advanced Virgo
interferometers. Exotic compact objects (ECOs) have been proposed that differ
from Kerr black holes, and which could leave an imprint upon the GW signal in a
variety of ways. Here we consider excitations of ECOs during inspiral, which
may occur when the monotonically increasing GW frequency matches a resonant
frequency of an exotic object. This causes orbital energy to be taken away,
leading to a speed-up of the orbital phase evolution. We show that resonances
with induced phase shifts $\lesssim 10$ radians can be detectable with
second-generation interferometers, using Bayesian model selection. We apply our
methodology to detections in the GWTC-1 catalog from the first and second
observing runs of Advanced LIGO and Advanced Virgo, finding consistency with
the binary black hole nature of the sources.
