An artificial molecule formed by two tunnel-coupled quantum dots in a GaAs/
AlxGa1-xAs heterostructure is studied in perpendicular magnetic fields. Cou
lomb blockade spectroscopy at low temperatures determines how the binding e
nergy of the artificial molecule evolves with magnetic field. The binding e
nergy and the double-dot ground-state energy exhibit mesoscopic fluctuation
s due to the coupling of electron wave functions on the individual dots.