Sensors and monitors for a physiological monitoring system having capability to indicate an accuracy of an estimated physiological condition. The sensor senses at least one physiological characteristic of a patient and is connectable to a monitor that estimates the physiological condition from signals detected by the sensor. The sensor includes a detector for detecting the signals from the patient which are indicative of the physiological characteristic. The sensor is associated with a memory configured to store data that defines at least one sensor signal specification boundary for the detected signals. The boundary is indicative of a quality of the signals and an accuracy of the physiological characteristic estimated from the signals by the monitor. The sensor further includes means for providing access to the memory to allow transmission of the data that defines the at least one sensor boundary to the monitor.