Abstract: Within an effective field theory approach, the potential of
discovering new physics searching for lepton flavour violating (LFV)
decays of Z bosons and quarkonia is discussed. In particular, the
expected sensitivities of future high-energy e+e- colliders
(FCC-ee/CEPC) and flavour factories are compared with indirect limits
set on these processes by LFV muon and tau decays.