We present high resolution, echelle spectroscopy of the close pre-main-sequence binary star systems DQ Tau and UZ Tau-E. Over a 16 day time interval we acquired 14 nights of spectra for DQ Tau and 12 nights of spectra for UZ Tau-E. This represents the entire orbital phase of DQ Tau, and 63 percent of that for UZ Tau-E. As expected, photospheric lines such as Li I lambda6707 clearly split into two components as the primary and secondary orbit one another, as did the permitted line He I lambda5876. Unlike the photospheric features, in both objects the forbidden lines of [O I] lambda6300, which has both a low-velocity and high-velocity component, and [O I] lambda5577, which has primarily a low-velocity component, retain the same shape throughout the orbit. Therefore these lines must originate outside of the immediate vicinity of the two stars and any gas that participates in the orbital motion of the stars.