  The prospects for shielding ultracold, paramagnetic, dipolar molecules from
inelastic and chemical collisions are investigated. Molecules placed in their
first rotationally excited states are found to exhibit effective long-range
repulsion for applied electric fields above a certain critical value, as
previously shown for non-paramagnetic molecules. This repulsion can safely
allow the molecules to scatter while reducing the risk of inelastic or
chemically reactive collisions. Several molecular species of $^2\Sigma$
molecules of experimental interest -- RbSr, SrF, BaF, and YO -- are considered,
and all are shown to exhibit orders of magnitude suppression in quenching rates
in a sufficiently strong laboratory electric field. It is further shown that,
for these molecules described by Hund's coupling case b, electronic and nuclear
spins play the role of spectator with respect to the shielding.
