  We show that the supersymmetric partition function of three-dimensional N=2
R-symmetric Chern-Simons-matter theories on the squashed S^3 and on S^2 x S^1
can be computed with the so-called Higgs branch localization method,
alternative to the more standard Coulomb branch localization. For theories that
could be completely Higgsed by Fayet-Iliopoulos terms, the path integral is
dominated by BPS vortex strings sitting at two circles in the geometry. In this
way, the partition function directly takes the form of a sum, over a finite
number of points on the classical Coulomb branch, of a vortex-string times an
antivortex-string partition functions.
