  Self-dual configurations of 2n points in a projective space of dimension n-1
were studied by Coble, Dolgachev-Ortland, and Eisenbud-Popescu. We examine the
self-dual matroids and self-dual valuated matroids defined by such
configurations, with a focus on those arising from hyperplane sections of
canonical curves. These objects are parametrized by the self-dual Grassmannian
and its tropicalization. We tabulate all self-dual matroids up to rank 5 and
investigate their realization spaces. Following Bath, Mukai, and Petrakiev, we
explore algorithms for recovering a curve from the configuration. A detailed
analysis is given for self-dual matroids arising from graph curves.
