We present a state-of-the-art study of the optical properties of free-standing silicene and of single-layer Si 1D and 2D nanostructures supported on Ag(110) and Ag(111) substrates. Ab initio simulations of reflectance anisotropy spectroscopy (RAS) and surface differential reflectivity spectroscopy (SDRS) applied to the clean Ag surface and Si/Ag interfaces are compared with new measurements. For Si/Ag(110) we confirm a pentagonal nanoribbon geometry, strongly bonded to the substrate, and rule out competing zigzag chain and silicenelike models. For Si/Ag(111) we reproduce the main experimental features and isolate the optical signal of the epitaxial silicene overlayer. The absorption spectrum of a silicene sheet computed including excitonic and local field effects is found to be quite similar to that calculated within an independent particle approximation, and shows strong modifications when adsorbed on a Ag substrate. Important details of the computational approach are examined and the origins of the RAS and SDRS signals are explained in terms of the interface and substrate response functions. Our study does not find any evidence for Si adlayers that retain the properties of freestanding silicene.