The recently developed in-column monochromators make it possible to record energy-c spectra with resolutions better than 30 meV from nanometer-sized regions. It should therefore in principle be possible to detect localized vibrational excitations. The scattering geometry in the electron microscope means that bond stretching in the specimen plane or longitudinal optic phonons dominate the scattering. Most promising for initial studies are vibrations with energies between 300 and 400 meV from hydrogen bonded to other atoms. Estimates of the scattering cross-sections on the basis of a simple model show that they are about the same as inner shell scattering cross-sections. Cross-sections also increase with charge transfer between the atoms, and theory incorporating realistic charge distributions shows that signal/noise is the only limitation to high-resolution imaging. Given the magnitude of the scattering cross-sections, minimizing the tail of the zero-loss peak is just as important as achieving a small-width at half-maximum. Improvements in both resolution and controlling the zero-loss tail will be necessary before it is practical to detect optic phonons in solids between 40 and 60 meV.