Summary: The finite element approximation on curved boundaries using parametric Raviart-Thomas spaces is studied in the context of the mixed formulation of Poisson’s equation as a saddle-point system. It is shown that optimal-order convergence is retained on domains with piecewise \(C^{k+2}\) boundary for the parametric Raviart-Thomas space of degree \(k\geq 0\) under the usual regularity assumptions. This extends the analysis of the first author et al. [ibid. 52, No. 6, 3165–3180 (2014; Zbl 1312.65184)] from the first-order system least squares formulation to mixed approaches of saddle-point type. In addition, a detailed proof of the crucial estimate in three dimensions is given which handles some complications not present in the two-dimensional case. Moreover, the appropriate treatment of inhomogeneous flux boundary conditions is discussed. The results are confirmed by computational results which also demonstrate that optimal-order convergence is not achieved, in general, if standard Raviart-Thomas elements are used instead of the parametric spaces.