This paper presents a detailed study of the deflection phenomena of a 400 GeV=c proton beam impinging on a new generation of bent silicon crystals; the tests have been performed at the CERN Super Proton Synchrotron H8 beam line. Channeling and volume reflection angles are measured with an extremely precise goniometer and with high resolution silicon microstrip detectors. Volume reflection has been observed and measured for the first time at this energy, with a single-pass efficiency as large as 98%, in good agreement with the simulation results. This efficiency makes volume reflection a possible candidate for collimation with bent crystals at the CERN Large Hadron Collider.