A superconducting quantum interference device (SQUID) was prepared on a micron-sized single crystal using a selected growth domain of a thin film of $CeCoIn_5$ grown by molecular beam epitaxy. SQUID voltage oscillations of good quality were obtained as well as interference effects stemming from the individual Josephson microbridges. The transport characteristics in the superconducting state exhibited several peculiarities which we ascribe to the periodic motion of vortices in the microbridges. The temperature dependence of the Josephson critical current shows good correspondence to the Ambegaokar-Baratoff relation, expected for the ideal Josephson junction. The results indicate a promising pathway to identify the type of order parameter in $CeCoIn_5$ by means of phase-sensitive measurements on microbridges.
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