A new method for dealing with electron tomography data from incomplete projection sets is proposed. The approach is inspired by exemplar-based inpainting techniques in image processing  and heuristically generates data for missing projection directions. The method has also been extended to work on three dimensional data. In general, electron tomography reconstructions suffer from elongation artifacts along the beam direction at 0° tilt. These artifacts can be seen in the corresponding Fourier domain as a missing wedge. The new method synthetically generates projections for these missing directions with the help of a dictionary-based approach that is able to convey both structure and texture at the same time. It constitutes a preprocessing step that can be combined with any tomographic reconstruction algorithm. The new algorithm was applied to the well-known Shepp-Logan phantom. Visually, the synthetic projections, reconstructions, and corresponding Fourier power spectra showed a decrease of the typical missing wedge artifacts. Quantitatively, the inpainting method is capable to reduce missing wedge artifacts and improves tomogram quality with respect to several figures-of-merit.