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From digital communications to satellite navigation, remotely synchronized clocks play a role of primary importance. The failure of these clocks will lead to not only service interruptions, but also, in some cases involving satellite navigation, more dire consequences with potential loss of life. Consequently, ensuring the integrity of remote clocks is now an issue of considerable import. In this paper, we demonstrate that an atomic clock can autonomously assess its own frequency stability and integrity by comparing the phase of its output signal to a delayed version of itself in what is essentially an interferometric technique. Using a high-quality crystal oscillator, we demonstrate that fractional frequency jumps of 10-11 are easily observed and that a cesium atomic clock's short-term Allan deviation can be measured without reference to another standard in a fully autonomous manner.