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Abstract: Atacama Large Millimeter/submillimeter Array observations have shown that candidate “post-starburst” galaxies (PSBs) at z~0.6 can retain significant molecular gas reservoirs. These results would imply that—unlike many model predictions—galaxies can shut down their star formation before their cold gas reservoirs are depleted. However, these studies inferred star formation rates (SFRs) either from [OII] line fluxes or from spectral energy distribution (SED) modeling and could have missed large dust-obscured contributions to the SFRs. In this study, we present Keck/NIRES observations of 13 massive (M_* >= 10^11M_⊙) PSBs, which allow us to estimate Hα SFRs in these gas-rich PSBs. We confirm the previously inferred low SFRs for the majority of the sample: 11/13 targets show clear Hα absorption, with minimal infilling indicating dust-corrected SFRs of <4.1Msun/yr. These SFRs are notably low given the large H2 reservoirs (∼(1–5) × 10^10Msun) present in 5/13 of these galaxies, placing them significantly offset from star-forming galaxies on the Kennicutt–Schmidt relation for star-forming galaxies. The [NII]/Hα ratios of all 13 PSBs imply contributions from non-star-forming ionization mechanisms (e.g., active galactic nuclei, shocks, or hot evolved stars) to their Hα emission, suggesting that even these low ongoing SFRs may be overestimated. These low Hα SFRs, dust corrected using Av estimates from SED fitting, confirm that these galaxies are very likely quiescent and, thus, that galaxies can quench before their cold gas reservoirs are fully depleted.