We present an accurate first-principles calculation of the quasiparticle electronic band structure of Si-34 and C-34 clathrates. Within the GW approximation, we find that Si-34 is a 1.85 direct band gap material. The reciprocal and real space dependence of the static dielectric function of Si-34 are provided. Further, we show by studying Xe-8@Si-46 that doping of Si-46 can lead to green-light semiconducting compounds, confirming that Si-clathrates are promising materials for optoelectronic applications. We finally predict the electronic properties of the hypothetical C-34 and C-46 phases within the same quasiparticle approach.