Majorana neutrinos may have transitional dipole moments, which violate lepton number as well as lepton flavour. We estimate the sensitivity of future colliders to the electron-muon neutrino dipole moment, $\lambda_{e\mu}$, by considering same-sign dilepton final states. We find that hadron colliders, even the proposed FCC-hh upgrade, are sensitive only to $|\lambda_{e\mu}|\gtrsim 10^{-9}\mu_B$ (with $\mu_B$ the Bohr magneton), a value two-three orders of magnitude larger than current bounds from astrophysics and low-energy neutrino-scattering experiments. In the case of a future muon collider, we show that the sensitivity varies from $|\lambda_{e\mu}|\sim 5\cdot 10^{-9}\mu_B$ for energy $\sqrt{s}\simeq 3$ TeV, to $\sim 10^{-12}\mu_B$ for $\sqrt{s}\simeq 50$ TeV, matching the current laboratory bounds for $\sqrt{s}\simeq 30$ TeV. The singular advantage of the muon collider signal would be a direct, clean identification of lepton number and flavour violation. We also show that a muon collider would improve by orders of magnitude the direct bounds on $m_{e\mu}$ and $m_{\mu\mu}$, two of the entries of the Majorana neutrino mass matrix. These bounds could be as strong as $\sim 50$ keV, still far above the neutrino mass scale.