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A stretchable pressure sensor is a necessary tool for perceiving physical interactions that take place on soft/deformable skins present in human bodies, prosthetic limbs, or soft robots. However, all existing types of stretchable pressure sensors have an inherent limitation, which is the interference of stretching with pressure sensing accuracy. Here, we present a design for a highly stretchable and highly sensitive pressure sensor that can provide unaltered sensing performance under stretching, which is realized through the synergistic creations of an ionic capacitive sensing mechanism and a mechanically hierarchical microstructure. Via this optimized structure, our sensor exhibits 98% strain insensitivity up to 50% strain and a low pressure detection limit of 0.2 Pa. With the capability to provide all the desired characteristics for quantitative pressure sensing on a deformable surface, this sensor has been used to realize the accurate sensation of physical interactions on human or soft robotic skin.