Massive young clusters (YCs) are expected to host intermediate-mass black holes (IMBHs) born via runaway collapse. These IMBHs are likely in binaries and can undergo mergers with other compact objects, such as stellar mass black holes (BHs) and neutron stars (NSs). We derive the frequency of such mergers starting from information available in the Local Universe. Mergers of IMBH-NS and IMBH-BH binaries are sources of gravitational waves (GWs), which might allow us to reveal the presence of IMBHs. We thus examine their detectability by current and future GW observatories, both ground- and space-based. In particular, as representative of different classes of instruments we consider Initial and Advanced LIGO, the Einstein gravitational-wave Telescope (ET) and the Laser Interferometer Space Antenna (LISA). We find that IMBH mergers are unlikely to be detected with instruments operating at the current sensitivity (Initial LIGO). LISA detections are disfavored by the mass range of IMBH-NS and IMBH-BH binaries: less than one event per year is expected to be observed by such instrument. Advanced LIGO is expected to observe a few merger events involving IMBH binaries in a 1-year long observation. Advanced LIGO is particularly suited for mergers of relatively light IMBHs (~100 Msun) with stellar mass BHs. The number of mergers detectable with ET is much larger: tens (hundreds) of IMBH-NS (IMBH-BH) mergers might be observed per year, according to the runaway collapse scenario for the formation of IMBHs. We note that our results are affected by large uncertainties, produced by poor observational constraints on many of the physical processes involved in this study, such as the evolution of the YC density with redshift.