Topological quantum computation using non-Abelian anyons provides a promising way of implementing universal quantum computation in an inherently fault-tolerant framework. At finite temperatures however, this inherent fault-tolerance must be supplemented with an active error correcting protocol. Recent progress in error correction for non-Abelian anyons has been made, but an explicit microscopic error correcting protocol based on non-Abelian anyons is still lacking. In this proposed research project, we aim to utilize the framework of tensor network states to perform the first construction and simulation of microscopic models for non-Abelian quantum error correction. Microscopic error correcting codes will be constructed from topologically ordered lattice models supporting non-Abelian anyons. Using tensor network methods, the process of error correction will be simulated in order to determine the accuracy threshold for these codes. Adopting suitable boundary conditions for topologically ordered lattice models, non-Abelian error correcting codes with a planar geometry will be constructed. The connection between the accuracy threshold and phase transitions in critical systems will be investigated for the non-Abelian case. Finally, the results will be extended to a fault-tolerant setting, allowing for faulty syndrome measurements. These results would eventually contribute towards the experimental realization of topological quantum computation.