The measurement of emittance in space-charge dominated, high brightness beam systems is investigated from conceptual, computational, and experimental viewpoints. As the self-field-induced collective motion in the low energy, high brightness beams emitted from photoinjector rf guns are more important in determining the macroscopic beam evolution than thermal spreads in transverse velocity; traditional methods for phase space diagnosis fail in these systems. We discuss the role of space charge forces in a traditional measurement of transverse emittance, the quadrupole scan. The mitigation of these effects by use of multislit- or pepper-pot-based techniques is explained. The results of a direct experimental comparison between quadrupole scanning and slit-based determination of the emittance of a 5 MeV high brightness electron beam are presented. These data are interpreted with the aid of both envelope and multiparticle simulation codes. It is shown that the ratio of the beam's $\ensuremath{\beta}$ function to its transverse plasma wavelength plays a central role in the quadrupole scan results. Methods of determining the presence of systematic errors in quadrupole scan data are discussed.