A characteristic feature of string theory is the asymptotic nature of the free energy genus expansion indicating the presence of non-perturbative effects due to branes. In certain toy models, such as minimal models or topological strings, the theory admits a matrix model description. In these cases the non-perturbative effects can be interpreted in terms of eigenvalues tunneling in the dual matrix model and the finite N matrix model can be naturally regarded as the non-perturbative completion of the theory. We address the case of the topological string on the Resolved Conifold. We compute the exact non-perturbative contribution to the free energy via Borel analysis and show how it controls the large order behavior of the theory. We interpreted the non-perturbative effects in the dual Chern-Simons matrix models and in the space-time in terms of toric branes.