Estimating the Center of Pressure (CoP) under legged robots is useful to control their posture and gait. This is traditionally done using contact sensors at the base of the foot or with sensors on distal joints, which are subject to wear and damage due to impulse forces. In vertebrates, skin and ligament deformation at the ankle is a particularly rich source of sensory information for locomotion. For our bipedal mechanism, afferent signals from sensors on synthetic skin wrapped around the ankles sufficed to estimate the location of the CoP with a mean accuracy >81.5%. For this we used K-Nearest Neighbors (KNN) algorithm trained on the same force magnitude applied at four and nine ground-truth CoP locations. For a single mechanical foot (i.e., single stance), signals from skin or ligaments (i.e., elastic rubber sheets and cables, respectively) also sufficed to calculate the CoP (Mean prediction accuracy >91.3%). Moreover, the visco-elasticity of these elements serves to passively stabilize the ankle. Importantly, training the single leg case with forces of different magnitudes also resulted in similarly accurate mean CoP prediction accuracy >84.5%. We show that using bio-inspired proprioceptive skins and/or ligament arrangements can provide reliable COP predictions, while permitting arbitrary postures of the ankle and no sensors on the sole of the foot prone to wear and damage. This novel approach to estimation of the CoP can be used to improve locomotion control in a new class of bio-inspired rigid, soft and hybrid (soft-rigid) legged robots.