We investigated the contact behaviors of a nanoscopic stiff thin film bonded to a compliant substrate and derived an analytical solution for determining the elastic modulus of thin films. Microscopic contact deformations of the gold and polydopamine thin films (<200 nm) coated on polydimethylsiloxane elastomers were measured by indenting a soft tip and analyzed in the framework of the classical plate theory and Johnson-Kendall-Roberts (JKR) contact mechanics. The analysis of this thin film contact mechanics focused on the bending and stretching resistance of thin films and is fundamentally different from conventional indentation measurements where the focus is on the fracture and compression of the films. The analytical solution of the elastic modulus of nanoscopic thin films was validated experimentally using 50 and 100 nm gold thin films coated on polydimethylsiloxane elastomers. The technical application of this analysis was further demonstrated by measuring the elastic modulus of thin films of polydopamine, a recently discovered biomimetic universal coating material. Furthermore, the method presented here is able to quantify the contact behaviors of nanoscopic thin films, effectively providing fundamental design parameters, the elastic modulus, and the work of adhesion, crucial for transferring them effectively into practical applications.