A search for the lepton-flavour violating decays B0 -> K*0µ(±)e(∓) and B(s)0-> ϕµ(±)e(∓) is presented, using proton-proton collision data collected by the LHCb detector at the LHC, corresponding to an integrated luminosity of 9 fb(-1). No significant signals are observed and upper limits of [see Image] are set at 90% (95%) confidence level. These results constitute the world's most stringent limits to date, with the limit on the decay B(s)0 -> ϕµ(±)e(∓) the first being set. In addition, limits are reported for scalar and left-handed lepton-flavour violating New Physics scenarios.