We report a high fidelity tomographic reconstruction of the quantum state of photon pairs generated by parametric down-conversion with orbital angular momentum (OAM) entanglement. Our tomography method allows us to estimate an upper and lower bound for the entanglement between the down-converted photons. We investigate the two-dimensional state subspace defined by the OAM states +/-l and superpositions thereof, with l = 1, 2, ... , 30. We find that the reconstructed density matrix, even for OAMs up to around l = 20, is close to that of a maximally entangled Bell state with a fidelity in the range between F = 0.979 and F = 0.814. This demonstrates that, although the single count-rate diminishes with increasing l, entanglement persists in a large dimensional state space.