Abstract A compact platform for cold atoms opens a range of exciting possibilities for portable, robust and accessible quantum sensors. In this work, we report on the development of a cold-atom microwave clock in a small package. Our work utilises the grating magneto-optical trap and high-contrast coherent population trapping in the lin ⊥ $perp $ lin polarisation scheme. We optically probe the atomic ground-state splitting of cold 87 Rb atoms using a Ramsey-like sequence whilst the atoms are in free-fall. We have measured a short-term fractional frequency stability of 5 × 10 − 11 / τ $5times10textasciicircum-11/sqrttau $ with a projected quantum projection noise limit at the 10 − 13 / τ $10textasciicircum-13/sqrttau $ level.