In this research, we investigate the electromagnetic behavior of a metallic thin-film with a periodic array of subwavelength apertures when dielectric objects are located on it. The influence of size, geometry and optical properties of the objects on the transmission spectra is numerically analyzed. We study the sensitivity of this system to changes in the refractive index of the illuminated volume induced by the presence of objects with sizes from hundreds of nanometers (submicron-sized objects) to a few microns (micron-sized objects). Parameters such as the object volume within the penetration depth of the surface plasmon in the buffer medium or the contact surface between the object and the nanostructured substrate strongly affect the sensitivity. The proposed system models the presence of objects and their detection through the spectral shifts undergone by the transmission spectra. Also, we demonstrate that these can be used for obtaining information about the refractive index of a micron-sized object immersed in a buffer and located on the nanostructured sensitive surface. We believe that results found in this study can help biomedical researchers and experimentalists in the process of detecting and monitoring biological organisms of large sizes (notably, cells).