In low-mass stars, chromospheric Hα emission is commonly used to probe the strength of the underlying magnetic field. Measuring this emission for members of open clusters, which have well-known ages, provides us with insight into the evolution of magnetic activity in these stars. We present the results of our spectroscopic surveys of members of two nearby, rich open clusters, Praesepe and the Hyades, which fold in updated membership catalogs for both based on Gaia data. Our data include 1200 of our own R ≈ 2000 spectra (900 for Praesepe, 300 for the Hyades), 300 archival spectra (270 for Praesepe, 30 for the Hyades), and more than 1000 spectra obtained by the Large Sky Area Multi-Object Fiber Spectroscopic Telescope (LAMOST; 760 for Praesepe and 300 for the Hyades). For each good-quality spectrum, we measure the Hα equivalent width and run a Monte Carlo iterator to estimate the uncertainty. Our surveys include at least one Hα measurement for 870 stars in Praesepe and for 460 stars in the Hyades. The vast majority of these are stars later than F7 (<1.2 M☉). Our coverage extends down to a spectral type of ≈M6 (≈0.2 M☉) in both clusters, allowing us to compare in detail the equivalent-width distributions for these two coeval populations (≈800 Myr). Our surveys represent the most extensive investigations of Hα emission in single-aged low-mass stellar populations to date, and form the basis of our exploration of the age-rotation-activity in these two benchmark clusters.