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• The reciprocity relationship between critical tuples of measurements and measuring units is addressed; • Efficient enumerative algorithms are proposed to identify criticalities of measurements from critical devices and vice versa; • The reduced capability to observe the system state is pointed out, which compromises the debugging of spurious measurements and precipitates unobservability. State estimation (SE) plays an essential role in energy management systems. It greatly depends on the availability of redundant, diverse, and strategically placed measurements. Insufficient supply of such measurements compromises SE, weakening its capability to detect/identify spurious data. Individual or group of measurements whose unavailability renders unobservability are termed critical for the SE. Similarly, one can characterize a single device or a group of them as critical, essential to the network observability, which means that the unavailability of the measurements these devices serve causes unobservability. This paper establishes the reciprocal relationship between critical tuples of measurements and measurement devices. Efficient enumerative algorithms are proposed to identify criticalities of measurements from critical devices and vice versa. Illustrative examples performed on the IEEE-30 bus system show how the proposed approach obtains adequate solutions for grid operation. [ABSTRACT FROM AUTHOR]