The stabilized contact lens methods and apparatus disclosed herein provide improved stabilization of a contact lens placed on a cornea of an eye. The contact lens comprises stabilization zones that allow the lens to repeatedly and consistently orient on the cornea such that a sensing zone located on the lower portion of the lens is located inferiorly to engage the lower eyelid. The stabilized contact lens can provide a lower pressure sensing zone with decreased thickness for pressure or other sensing related to the lower eyelid. The decreased thickness has the advantage of improving coupling between forces from an eyelid and a lower chamber of a fluidic module. The improved coupling allows increased amounts of fluid to move between the lower chamber and an upper optical chamber coupled to the lower chamber, such that the upper chamber can increase curvature and optical power in response to pressures of the eyelid.