Ultralight degrees of freedom coupled to matter lead to resonances, which can be excited when the Compton wavelength of the field equals a dynamical scale in the problem. For binaries composed of a star orbiting a supermassive black hole, these resonances lead to a smoking-gun effect: a periastron distance which stalls, even in the presence of gravitational-wave dissipation. This effect, also called a floating orbit, occurs for generic equatorial but eccentric orbits, and we argue that finite-size effects are not enough to suppress it.