In contrast to photometric transits, whose peak signal occurs at mid-transit due to occultation of the brightest region of the disk, polarimetric transits provide a signal upon ingress and egress due to occultation of the polarized stellar limb. Limb polarization, the bright corollary to limb darkening, arises from the $90^circ$ scattering angle and low optical depth experienced by photons at the limb. In addition to the ratio $R_{rm p} / R_*$, the amplitude of a polarimetric transit is expected to be controlled by the strength and width of the stellar limb polarization profile, which depend on the scattering-to-total opacity ratio at the stellar limb. We present a short list of the systems providing the highest expected signal-to-noise ratio for detection of this effect, and we draw particular attention to HD 80606b. This planet is spin/orbit misaligned, has a three-hour ingress, and has a bright parent star, which make it an attractive target. We report on test observations of an HD 80606b ingress with the POLISH2 polarimeter at the Lick Observatory Shane 3-m telescope. We conclude that unmodeled telescope systematic effects prevented polarimetric detection of this event. We outline a roadmap for further refinements of exoplanet polarimetry, whose eventual success will require a further factor of ten reduction in systematic noise.
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