ABSTRACT When embedded in dense cluster cores, intermediate-mass black holes (IMBHs) acquire close stellar or stellar-remnant companions. These companions are not only gravitationally bound, but also tend to hierarchically isolate from other cluster stars through series of multibody encounters. In this paper we study the demographics of IMBH companions in compact star clusters through direct N-body simulations. We study clusters initially composed of 105 or 2 × 105 stars with IMBHs of 75 and 150 solar masses, and we follow their evolution for 6–10 Gyr. A tight, innermost binary pair of IMBH and stellar object rapidly forms. The IMBH has a companion with an orbital semimajor axis at least three times tighter than the second-most-bound object over 90% of the time. These companionships have typical periods on the order of years and are subject to cycles of exchange and destruction. The most frequently observed, long-lived pairings persist for ∼107 years. The demographics of IMBH companions in clusters are diverse: they include both main-sequence, giant stars and stellar remnants. Companion objects may reveal the presence of an IMBH in a cluster in one of several ways. The most-bound companion stars routinely suffer grazing tidal interactions with the IMBH, offering a dynamical mechanism to produce repeated flaring episodes like those seen in the IMBH candidate HLX-1. The stellar winds of companion stars provide a minimum quiescent accretion rate for IMBHs, with implications for radio searches for IMBH accretion in globular clusters. Finally, gravitational wave inspirals of compact objects occur with promising frequency.