We present the results of 2D and 3D magnetohydrodynamical numerical simulations of relativistic magnetic reconnection, with particular emphasis on the dynamics of the plasma in a Petschek-type configuration with high Lundquist numbers, S˜ 105-108. The numerical scheme adopted, allowing for unprecedented accuracy for this type of calculations, is based on high-order finite volume and discontinuous Galerkin methods as recently proposed by Dumbser & Zanotti. The possibility of producing high Lorentz factors is discussed, showing that Lorentz factors close to ˜4 can be produced for a plasma parameter σm= 20. Moreover, we find that the Sweet-Parker layers are unstable, generating secondary magnetic islands, but only for S > Sc˜ 108, much larger than what is reported in the Newtonian regime. Finally, the effects of a mildly anisotropic Ohm's law are considered in a configuration with a guide magnetic field. Such effects produce only slightly faster reconnection rates and Lorentz factors of about 1 per cent larger with respect to the perfectly isotropic Ohm's law.