A measurement of the differential branching fraction of the decay B 0 → K ∗(892)0 μ + μ − is presented together with a determination of the S-wave fraction of the K + π − system in the decay B 0 → K +π− μ + μ −. The analysis is based on pp-collision data corresponding to an integrated luminosity of 3 fb−1 collected with the LHCb experiment. The measurements are made in bins of the invariant mass squared of the dimuon system, q 2. Precise theoretical predictions for the differential branching fraction of B 0 → K ∗(892)0 μ + μ − decays are available for the q 2 region 1.1 < q 2 < 6.0 GeV2 /c 4. In this q 2 region, for the K +π− invariant mass range 796 < m Kπ < 996 MeV/c 2, the S-wave fraction of the K +π− system in B 0 → K +π− μ + μ − decays is found to be FS=0.101±0.017(stat)±0.009(syst), FS=0.101±0.017(stat)±0.009(syst), and the differential branching fraction of B 0 → K ∗(892)0 μ + μ − decays is determined to be dB/dq2=(0.392+0.020−0.019(stat)±0.010(syst)±0.027(norm))×10−7c4/GeV2. dB/dq2=(0.392−0.019+0.020(stat)±0.010(syst)±0.027(norm))×10−7c4/GeV2. The differential branching fraction measurements presented are the most precise to date and are found to be in agreement with Standard Model predictions.