Example eye-mountable devices and methods for placing a flexible ring containing electronics in an eye-mountable device are described. A method may involve forming a first polymer layer, which defines a posterior side of an eye-mountable device. Further, the method may involve positioning a ring-shaped structure on the first polymer layer in a predetermined rotational orientation, wherein the ring-shaped structure comprises a sensor configured to detect an analyte. Still further, the method may involve forming a second polymer layer over the first polymer layer and the ring-shaped structure, such that the ring-shaped structure is fully enclosed by the first polymer layer and the second polymer layer. The second polymer layer defines an anterior side of the eye-mountable device. The method may also involve forming a channel through the second polymer layer based on the predetermined rotational orientation, such that the sensor is configured to receive the analyte via the channel.