Fluorine-19 magnetic shielding tensors have been measured in a series of actinide tetrafluorides (AnF4) by solid state nuclear magnetic resonance spectroscopy. Tetravalent actinide centers with 0-8 valence electrons can form tetrafluorides with the same monoclinic structure type, making these compounds an attractive choice for a systematic study of the variation in the electronic structure across the 5f row of the Periodic Table. Pronounced deviations from predictions based on localized valence electron models have been detected by these experiments, which suggests that this approach may be used as a quantitative probe of electronic correlations.