We analyse the impact of future hard X-ray observations on the search for indirect signatures of particle dark matter in large extragalactic systems such as nearby clusters or groups of galaxies. We argue that the hard X-ray energy band falls squarely at the peak of the inverse-Compton emission from electrons and positrons produced by dark matter annihilation or decay for a large class of dark matter models. Specifically, the most promising are low-mass models with a hard electron–positron annihilation final state spectrum and intermediate-mass models with a soft electron–positron spectrum. We find that constraints on dark matter models similar to the current constraints from the Fermi Gamma-ray Space Telescope will be close to the sensitivity limit of the near-term hard X-ray telescopes Nuclear Spectroscopic Telescope Array (NuSTAR) and Astro-H for relatively long observations. An instrument like the Wide Field Imager proposed for Advanced Telescope for High ENergy Astrophysics (ATHENA) would instead give a significant gain in sensitivity to dark matter if placed in a low background orbit similar to NuSTAR’s; however, given the higher expected background level for ATHENA’s proposed orbit at L2, its sensitivity will be similar to that of NuSTAR.