Can reactions produce microwave or radio wave radiation?
An ammonia maser qualifies as an inorganic RF-emitting reaction. As the nitrogen changes position in the $\ce{NH3}$ molecule, ~24 GHz radiation is emitted.

Similarly, organic methanol, $\ce{CH3OH}$ makes a maser found in nature, emitting at ~36.2 GHz and also at ~6.7 GHz.

BTW, if the reactants are  moving away rapidly (e.g. interstellar gases), visible radiation is red-shifted to microwaves... or lower, so wavelength depends on your frame of reference. So, as Brumley and Stevens state, listen in to radio astronomy.

Though these might be due to physical excitation, and not an exact answer for your question, an interesting experiment would be to form $\ce{NH3}$, e.g. with the Haber process, and try to detect the 24 GHz radiation, perhaps due to initial formation of the molecule in a metastable state, or due to rearrangement. A similar experiment could be done with methanol, forming it from $\ce{CO}$ and $\ce{H2}$, looking for 36.2 GHz or 6.7GHz signals. I'd be very interested to know if you or anyone else tries that!