On July 10, 2010, the ROSETTA spacecraft performed a flyby at asteroid (21)Lutetia at a solar distance of 2.72 AU. The spacecraft-asteroid distance at closest approach was 3120 km. The magnetometers onboard ROSETTA were operating but did not detect any conclusive signature of the asteroid. Any magnetic field signature which could possibly be attributed to the asteroid was below 1 nT. Consequently an upper limit for the global magnetic properties of asteroid (21)Lutetia could be derived: maximum dipole moment ≤1.0×1012Am2, global maximum magnetization ≤2.1×10-3A/m, specific moment ≤5.9×10-7Am2/kg. Draping of magnetic fields around the nucleus was sought, but evidence for this could not be clearly identified in the data. Plasma simulations taking into account the estimated upper limit of the magnetization and possible outgassing revealed interesting structures very close to the asteroid. The results obtained at Lutetia are contrasted with the results of other asteroid flyby results.