This paper presents a contactless methodology for determining all independent elastic-stiffness coefficients C i j of a transverse isotropic thin film: C 1 1 , C 1 2 , C 1 3 , C 3 3 , and C 4 4 . The electromagnetic-acoustic-resonance technique measures the acoustic resonance frequencies of a film-coated specimen with a high accuracy, better than 10 - 5 , which enables determining the film C i j with the known substrate C i j . The measurement takes two steps. First, through-thickness resonance frequencies of longitudinal and shear modes are measured to determine C 3 3 and C 4 4 , and the film thickness. Then, remaining three coefficients are deduced from measurements of the free-vibration resonance frequencies of the layer parallelepiped specimen. Simulations and experiments with monocrystal copper and titanium confirm the reliability of the resultant film C i j within 5%, when the film thickness is more than 0.5% of the substrate.