  Certifying individual quantum devices with minimal assumptions is crucial for
the development of quantum technologies. Here, we investigate how to leverage
single-system contextuality to realize self-testing. We develop a robust
self-testing protocol based on the simplest contextuality witness for the
simplest contextual quantum system, the Klyachko-Can-Binicio\u{g}lu-Shumovsky
(KCBS) inequality for the qutrit. We establish a lower bound on the fidelity of
the state and the measurements (to an ideal configuration) as a function of the
value of the witness under a pragmatic assumption on the measurements we call
the KCBS orthogonality condition. We apply the method in an experiment with
randomly chosen measurements on a single trapped $^{40}{\rm Ca}^+$ and
near-perfect detection efficiency. The observed statistics allow us to
self-test the system and provide the first experimental demonstration of
quantum self-testing of a single system. Further, we quantify and report that
deviations from our assumptions are minimal, an aspect previously overlooked by
contextuality experiments.
