In this article we study b → sµ + µ − transitions and possible correlations with the anomalous magnetic moment of the muon (a µ ) within two-Higgs-doublet models with generic Yukawa couplings, including the possibility of right-handed neutrinos. We perform the matching on the relevant effective Hamiltonian and calculate the leading one-loop effects for b → s ( ) , b → sγ, ∆B = ∆S = 2, b → sνν and → γ transitions in a general R ξ gauge. Concerning the phenomenology, we find that an explanation of the hints for new physics in b → sµ + µ − data is possible once right-handed neutrinos are included. If lepton flavour violating couplings are allowed, one can account for the discrepancy in a µ as well. However, only a small portion of parameter space gives a good fit to b → sµ + µ − data and the current bound on h → τ µ requires the mixing between the neutral Higgses to be very small if one aims at an explanation of a µ .