The search for the production of weakly-interacting SUSY particles at the LHC is crucial for testing supersymmetry in relation to dark matter. Decays of neutralinos into Higgs bosons occur over some significant part of the SUSY parameter space and represent the most important source of $h$ boson production in SUSY decay chains in the MSSM. We study h production in neutralino decays using scans of the phenomenological MSSM. Whilst in constrained MSSM scenarios the decay chi^0_2 -> h chi^0_1 is the dominant channel, this does not hold in more general MSSM scenarios. On the other hand, the chi^0_2,3 -> h chi^0_1 decays remain important and are highly complementary to multi-lepton final states in the LHC searches. The perspectives for the LHC analyses at 8 and 14 TeV as well as the reach of an e+e- collider at 0.5, 1, 1.5 and 3 TeV are discussed.
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