An eye-mountable device includes layer(s) of polymer material defining a body. The body includes a first side and a second side extending from a first end to a second end. The first side opposes the second side and curves inwardly toward the second side. The second side curves outwardly away from the first side. The body includes an anterior surface and a posterior surface extending from the first side to the second side and from the first end to the second end. The anterior side opposes the posterior side. The posterior surface has a concave shape. The device includes a substrate in the body including a mounting platform disposed proximally to a middle of the second side. The device includes, on the mounting platform, electronics that interact with a biological environment and monitor health-related information. The body may have a thickness profile that prevents the device from undesired movement.