Superconducting MgB ₂ films with T _c=38.6  K were prepared using a precursor-deposition, ex situ postprocessing approach. Precursor films of boron, ∼0.5 μm thick, were deposited onto Al ₂ O ₃ (102) substrates by electron-beam evaporation; a postanneal at 890 °C in the presence of bulk MgB ₂ and Mg metal produced highly crystalline MgB ₂ films. X-ray diffraction indicated that the films exhibit some degree of c-axis alignment, but are randomly oriented in plane. Transport current measurements of the superconducting properties show high values of the critical current density and yield an irreversibility line that exceeds that determined by magnetic measurements on bulk polycrystalline materials. © 2001 American Institute of Physics.