The e + e − → p ¯ p cross section and the proton magnetic form factor have been measured in the center-of-mass energy range from 3.0 to 6.5 GeV using the initial-state radiation technique with an undetected photon. This is the first measurement of the form factor at energies higher than 4.5 GeV. The analysis is based on 469     fb − 1 of integrated luminosity collected with the BABAR detector at the PEP-II collider at e + e − center-of-mass energies near 10.6 GeV. The branching fractions for the decays J / ψ → p ¯ p and ψ ( 2 S ) → p ¯ p have also been measured.