  We demonstrate coherent microwave control of the rotational, hyperfine and
Zeeman states of ultracold CaF molecules, and the magnetic trapping of these
molecules in a single, selectable quantum state. We trap about $5\times 10^{3}$
molecules for 2 s at a temperature of 65(11) $\mu$K and a density of $1.2
\times 10^{5}$ cm$^{-3}$. We measure the state-specific loss rate due to
collisions with background helium.
