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The melting transition of anisotropic two-dimensional crystals is studied in a model system of superparamagnetic colloids confined to a water-air interface. The anisotropy of the induced dipole-dipole interaction is varied by tilting the external magnetic field off the normal to the particle plane leading to a centered rectangular crystal lattice. The melting of these crystals is controlled by decreasing the magnetic field strength and the phase transition is studied by the use of video microscopy in terms of defect formation. Similar to the isotropic case, which is described by the KTHNY-theory, the centered rectangular crystal melts via a quasi-hexatic phase. In case of large anisotropy the system melts along the direction of the in-plane field, whereas the order perpendicular to it remains crystal-like. The occurence of this new smectic-like phase can be explained by the orientation of defects in the system: Dislocations with a Burgers vector parallel to the in-plane component of the magnetic field are clearly preferred and one type of dislocation pair is completely suppressed.