  Polar molecules in superpositions of rotational states exhibit long-range
dipolar interactions, but maintaining their coherence in a trapped sample is a
challenge. We present calculations that show many laser-coolable molecules have
convenient rotational transitions that are exceptionally insensitive to
magnetic fields. We verify this experimentally for CaF where we find a
transition with sensitivity below 5 Hz G$^{-1}$ and use it to demonstrate a
rotational coherence time of 6.4(8) ms in a magnetic trap. Simulations suggest
it is feasible to extend this to more than 1 s using a smaller cloud in a
biased magnetic trap.

Atomic Physics