We consider the stability conditions for half-quantum vortices in a quasi-two-dimensional px+ipy superconductor (such as Sr2RuO4 is believed to be). The predicted exotic nature of these excitations has recently attracted much attention, but they have not been observed yet. We emphasize that an isolated half-quantum vortex has a divergent energy cost in the bulk due to its unscreened spin current, which requires two half-quantum vortices with opposite spin winding to pair. We show that the stability of such a pair is enhanced when the ratio of spin superfluid density to superfluid density ρsp/ρs is small. We propose using various mesoscopic geometries to stabilize and observe these exotic excitations.