In order to determine the mechanical properties of materials suitable for use as coatings on structural or gas turbine components, it is often necessary to conduct testing on coated specimens, with the properties of the coating then to be extracted from the response. A methodology for extracting material properties from comparisons of resonant frequencies and system loss factors for coated and uncoated beams, which is applicable even when the desired properties (storage and loss modulus) have a strong dependence on the amplitude of cyclic strain, is summarized and applied to the determination of the material properties of an air plasma sprayed alumina-titania blend ceramic to which a viscoelastic material has been added by vacuum infiltration. Tests were conducted at both room and elevated temperatures. Material properties obtained from specimens with three coating thicknesses are compared and show that values obtained for the stiffness (storage modulus) decrease with increasing coating thickness, but that values obtained for the measure of dissipative capacity (loss modulus) are essentially independent of thickness. Addition of the infiltrate was found to double the storage modulus and to increase the loss modulus at room temperature by factors of up to 3, depending on the amplitude of cyclic strain. The storage modulus of this infiltrated coating appears to diminish with increasing depth into the coating, suggesting dependence on the amount of infiltrate present. The loss modulus, however, appears to be comparatively insensitive to the amount of infiltrate present. Results from a limited investigation of the influence of increased temperature on the properties of the infiltrated coating show decreases in storage modulus with temperature, and a maximum in the loss modulus at a temperature determined by the temperature dependent properties of the specific viscoelastic material used as the infiltrate.