We examine the sensitivity at a future 100 TeV proton-proton collider to compressed dark sectors whose decay products are invisible due to below-threshold energies and/or small couplings to the Standard Model. Such a scenario could be relevant to models of WIMP dark matter, where the lightest New Physics state is an (isolated) electroweak multiplet whose lowest component is stable on collider timescales. We rely on the additional emission of a hard on-shell Z-boson decaying to leptons, a channel with low background systematics, and include a careful estimate of the real and fake backgrounds to this process in our analysis. We show that an integrated luminosity of 30 ab(-1) would allow exclusion of a TeV-scale compressed dark sector with inclusive production cross section 0.3 fb, for 1% background systematic uncertainty and splittings below 5 GeV. This translates to exclusion of a pure higgsino (wino) multiplet with mass of 500 (970) GeV.