Two fresnoitic glasses (2BaO-TiO_2 2GeO_2 and 2SrO-TiO_2-2SiO_2) are studied by high-resolution electron energy-loss spectroscopy in the transmission electron microscope. It is shown that coordination fingerprinting using the electron energy-loss near-edge structure (being widely used in crystalline compounds bearing transition metals) can also be applied to amorphous matter. In particular, respective ratios of fourfold, fivefold, and sixfold co-ordinated Ti^4+ are verified for both glasses in comparison to earlier X-ray photoemission measurements. The results demonstrate that - sufficiently high spectral resolution given - electron energy-loss spectroscopy in the transmission electron microscope is an extremely promising and powerful technique for atomistic-structure studies of amorphous materials. PACS 61.43.Fs, 79.20.Uv