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We study gravitational-wave emission from the quasi-circular, extreme massratio inspiral of compact objects of mass m0 into massive objects of mass M>>m0whose external metric is identical to the Schwarzschild metric, except for theabsence of an event horizon. To be specific we consider one of the simplestrealizations of such an object: a nonrotating thin-shell gravastar. The powerradiated in gravitational waves during the inspiral shows distinctive peakscorresponding to the excitation of the polar oscillation modes of thegravastar. For ultra-compact gravastars the frequency of these peaks dependsmildly on the gravastar compactness. For masses M~10^6Msun the peaks typicallylie within the optimal sensitivity bandwidth of LISA, potentially providing aunique signature of the horizonless nature of the central object. Forrelatively modest values of the gravastar compactness the radiated power haseven more peculiar features, carrying the signature of the microscopicproperties of the physical surface replacing the event horizon.

Gravitational-wave signatures of the absence of an event horizon. II. Extreme mass ratio inspirals in the spacetime of a thin-shell gravastar