We show that the precise orientation of a C-60 molecule which terminates the tip of a scanning probe microscope can be determined with atomic precision from submolecular contrast images of the fullerene cage. A comparison of experimental scanning tunneling microscopy data with images simulated using computationally inexpensive Huckel theory provides a robust method of identifying molecular rotation and tilt at the end of the probe microscope tip. Noncontact atomic force microscopy resolves the atoms of the C-60 cage closest to the surface for a range of molecular orientations at tip-sample separations where the molecule-substrate interaction potential is weakly attractive. Measurements of the C-60-C-60 pair potential acquired using a fullerene-terminated tip are in excellent agreement with theoretical predictions based on a pairwise summation of the van der Waals interactions between C atoms in each cage, i.e., the Girifalco potential [L. Girifalco, J. Phys. Chem. 95, 5370 (1991)].