Gaiotto introduced the notion of a conformal limit of a Higgs bundle and conjectured that these should identify the Hitchin component with the Oper stratum in the deRham moduli space. In the case of closed Riemann surfaces this result was proven by Dumitrescu, et al., and the limits were shown to exist much more generally by Collier and the speaker. In this talk I will report on progress in the case of parabolic Higgs bundles, which were the context of Gaiotto's original conjecture. This is joint work with B. Collier and L. Fredrickson.