  We compute by supersymmetric localization the expectation values of half-BPS
't Hooft line operators in $\mathcal{N}=2$ $U(N)$, $SO(N)$ and $USp(N)$ gauge
theories on $S^1 \times \mathbb{R}^3$ with an $\Omega$-deformation. We evaluate
the non-perturbative contributions due to monopole screening by calculating the
supersymmetric indices of the corresponding supersymmetric quantum mechanics,
which we obtain by realizing the gauge theories and the 't Hooft operators
using branes and orientifolds in type II string theories.
