Detection and quantification of myocardial scars are helpful for diagnosis of heart diseases and for personalized simulation models. Scar tissue is generally characterized by a different conduction of excitation. We aim at estimating conductivity-related parameters from endocardial mapping data. Solving this inverse problem requires computationally expensive monodomain simulations on fine discretizations. We aim at accelerating the estimation by combining electrophysiology models of different complexity. Distributed parameter estimation is performed by minimizing the misfit between simulated and measured electrical activity on the endocardial surface, subject to the monodomain model and regularization. We formulate this optimization problem, including the modelling of scar tissue and different regularizations, and design an efficient solver. We consider grid hierarchies and monodomain–eikonal model hierarchies in a recursive multilevel trust-region method. With numerical examples, efficiency and estimation quality, depending on the data, are investigated. The multilevel solver is significantly faster than a comparable single level solver. Endocardial mapping data of realistic density appears to be sufficient to provide quantitatively reasonable estimates of location, size, and shape of scars close to the endocardial surface.