Photoluminescence properties of a freestanding nanoporous SiC layer obtained from bulk 6H-SiC substrate as well as SiC nanopowder consisting of numerous separated nanoparticles has been investigated. The nanoporous SiC layer is obtained by UV radiation assisted electrochemical etching of the 6H-SiC wafer and the SiC nanopowder is formed by mechanical grinding of the nanoporous SiC free layer. A comparison of low temperature PL spectra of the SiC nanostructures and initial SiC bulk substrate has been performed. The evolution of PL spectra of the SiC nanostructures with respect to their surface states and excitation laser power has been studied. In particular, the well pronounced high energy tail above the excitonic bandgap in the PL spectra of the nanostructured SiC is attributed to quantum confinement effects. The strong PL signal obtained below the bandgap is explained by radiative transitions involving surface states, N-Al donoracceptor recombination levels and deep levels corresponding to volume defects in the SiC nanocrystallites.