The constituents of dark matter are still unknown, and the viable possibilities span a very large mass range. Specific scenarios for the origin of dark matter sharpen the focus to within about an MeV to 100 TeV. Most of the stable constituents of known matter have masses in this lower range, and a thermal origin for dark matter works in a simple and predictive manner. If there is a non-gravitational interaction between dark matter and ordinary matter, as there must be in the case of a thermal origin, then there is necessarily a production mechanism in accelerator-based experiments. NOvA is a high luminosity long-baseline neutrino oscillation experiment at Fermilab that is capable of searching for signatures of dark matter re-scattering with electrons in its near detector after production in the NuMI target. In this talk, I present an analysis to search for an excess of single-electron events in the NOvA near detector consistent with the presence of dark matter-electron scattering. I will also discuss a future search for sub-GeV dark matter with the Light Dark Matter eXperiment (LDMX), a planned electron-beam fixed-target missing-momentum search for dark matter at SLAC.