In joint work with Oscar García-Prada and Junming Zhang, we show the existence of compact connected components in relative character varieties of the fundamental group of the punctured sphere for real Lie groups of Hermitian type. Our approach uses the non-abelian Hodge correspondence exploiting elements of the general theory of Higgs bundles for these groups, which we extend to the parabolic bundle setting. This generalises previous results of Tholozan-Toulisse and Feng-Zhang.