Planet host stars with well-constrained ages provide a rare window to the time domain of planet formation and evolution. The NASA K2 mission has enabled the discovery of the vast majority of known planets transiting stars in clusters, providing a valuable sample of planets with known ages and radii. We present the discovery of two planets transiting K2-264, an M2 dwarf in the intermediate age (600-800 Myr) Praesepe open cluster (also known as the Beehive Cluster, M44, or NGC 2632), which was observed by K2 during Campaign 16. The planets have orbital periods of 5.8 and 19.7 d, and radii of 2.2 ± 0.2 and 2.7 ± 0.2R⊕, respectively, and their equilibrium temperatures are 496 ± 10 and 331 ± 7 K, making this a system of two warm sub-Neptunes. When placed in the context of known planets orbiting field stars of similar mass to K2-264, these planets do not appear to have significantly inflated radii, as has previously been noted for some cluster planets. As the second known system of multiple planets transiting a star in a cluster, K2-264 should be valuable for testing theories of photoevaporation in systems of multiple planets. Follow-up observations with current near-infrared (NIR) spectrographs could yield planet mass measurements, which would provide information about the mean densities and compositions of small planets soon after photoevaporation is expected to have finished. Follow-up NIR transit observations using Spitzer or large ground-based telescopes could yield improved radius estimates, further enhancing the characterization of these interesting planets.