In this contribution, focus is placed on titanium dioxide (TiO \(_{2}\) ) films, a few micrometers thick, produced through Pulsed Laser Deposition in the form of columnar elements surrounded by voids, coating a Silicon flat substrate. Our aim is to estimate the homogenized elastic properties of this nanostructured coating, possibly anisotropic, utilized in a variety of industrial contexts, and to optimize consistently the production process parameters such as the chamber pressure. A preliminary and comparative assessment is provided through two different procedures. (i) The first strategy, recently outlined in [1], rests on digital images of the coated samples acquired by a Scanning Electron Microscope with a nanometer resolution. Being the titanium dioxide in an amorphous state, an isotropic elastic behaviour is assumed for the matrix, with parameters derived from the literature. In agreement with classical homogenization procedures, the effective stiffness matrix is retrieved through a micro-macro approach on the basis of finite element analyses of a representative volume element, equipped with periodic boundary conditions and subjected to single components of the macroscopic strain tensor. These results, obtained for different coated samples, indicate with a good approximation an orthotropic, transversely – isotropic behavior. (ii) The second procedure exploits the information on bulk acoustic wave speeds probed by Brillouin inelastic scattering. This technique rests on a photon – phonon (opto – mechanical) process, exploiting the coupling between the local variations of the refraction index and the strain states induced by travelling acoustic waves, spontaneously related to the thermal agitation: the velocity of propagation of the acoustic waves within the coating is detected by analyzing the angular frequency of the scattered light beam, at varying the incident beam angle. Similarly to other approaches for composite materials, the propagation speeds of the bulk acoustic waves are utilized through inverse analysis to estimate the anisotropic apparent moduli of the thin film, entering the Christoffel equation.