We present parameter-free calculations of the frequency-dependent dielectric function in order to understand the optical properties of Si and Ge nanoparticles in a SiC matrix. The calculations are based upon a pseudopotential-plane-wave method. The dots are described by clusters LIP to 239 atoms embedded in cubic SiC or saturated by hydrogen to simulate a polytype with a wider energy gap. The resulting optical spectra are discussed in dependence on the dot size and dot surroundings.