High resolution ALMA CO (2-1) observations of the ram pressure stripped galaxies NGC 4402 in the Virgo cluster, and NGC 4921 in the Coma cluster, show some of the clearest evidence yet of the impact of ram pressure on the molecular ISM of galaxies. The leading side of NGC 4402, upon which ram pressure is incident, has a large extraplanar plume of material, also seen in HST observations of dust extinction. Molecular gas in the plume, which has a width and length of about 1 x 2 kpc, shows distinct non-circular motions as large as 80 km/s; these are the most extreme velocities in the galaxy and are likely the result of acceleration by ram pressure. We also detect some isolated clouds below the plume near the disk mid-plane. These clouds have velocities consistent with normal galactic rotation, and appear to be unaffected by ram pressure. We also find morphological and kinematic evidence of ram pressure compression of molecular gas in a region of intense star formation on the leading side just inside the plume, at slightly smaller galactocentric radius. It is possible star formation in this region is triggered by compression from the ram pressure. In NGC4921, the largest spiral in the Coma cluster, we are able to study the morphological effects of ram pressure on the dense ISM in even greater detail, due to the higher relative strength of ram pressure in Coma, and the fact that NGC 4921 is oriented nearly face-on. We detect distinct filaments of dense ISM in both CO (2-1) and HST dust. These filaments can be as long as 2 kpc, but are only about 200 pc wide, and are projected outward into the otherwise gas stripped region on the leading side, indicating that they have resisted stripping and decoupled from the surrounding gas. They also appear to have young star clusters at the head, seen with HST, possibly the result of compressed gas at the tips of the filaments. Along with the high density of the filaments, from comparison with structures in MHD simulations, we find evidence that these filaments may be supported against ram pressure by magnetic fields. In NGC 4402 we are able to study the large scale effects of ram pressure on the dense ISM, and in NGC 4921 we investigate in higher resolution the evolution of the individual dense ISM substructures under the force of compression and stripping.