We consider low-scale leptogenesis via right-handed neutrinos N coupled to a Z' boson, with gauged U(1)_B-L as a simple realization. Keeping the neutrinos sufficiently out of equilibrium puts strong bounds on the Z' coupling strength and mass, our focus being on light Z' and N, testable in the near future by SHiP, HPS, Belle II, and at the LHC. We show that leptogenesis could be robustly falsified in a large region of parameter space by the double observation of Z' and N, e.g. in the channel

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... Z' → NN with displaced N-decay vertex, and by several experiments searching for light Z', according to the mass of N.