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Polar molecules offer a new platform for quantum simulation of systems with long-range interactions, based on the electrostatic interaction between their electric dipole moments. Here, we report the development of coherent quantum state control using microwave fields in 40 Ca 19 F and 87 Rb 133 Cs molecules, a crucial ingredient for many quantum simulation applications. We perform Ramsey interferometry measurements with fringe spacings of∼ 1 kHz and investigate the dephasing time of a superposition of N= 0 and N= 1 rotational states when the molecules are confined. For both molecules, we show that a judicious choice of molecular hyperfine states minimises the impact of spatially varying transition-frequency shifts across the trap. For magnetically trapped 40 Ca 19 F we use a magnetically insensitive transition and observe a coherence time of 0.61 (3) ms. For optically trapped 87 Rb 133 Cs we exploit an …