A method for analysing the hadronic resonance contributions in B ¯ 0 → K ¯ ∗ 0 μ + μ - decays is presented. This method uses an empirical model that relies on measurements of the branching fractions and polarisation amplitudes of final states involving J PC = 1 - - resonances, relative to the short-distance component, across the full dimuon mass spectrum of B ¯ 0 → K ¯ ∗ 0 μ + μ - transitions. The model is in good agreement with existing calculations of hadronic non-local effects. The effect of this contribution to the angular observables is presented and it is demonstrated how the narrow resonances in the q 2 spectrum provide a dramatic enhancement to C P -violating effects in the short-distance amplitude. Finally, a study of the hadronic resonance effects on lepton universality ratios, R K ( ∗ ) , in the presence of new physics is presented.