In this work, we report the successful growth of high-quality epitaxial hematite (alpha-Fe2O3) thin films on three different substrates: (0001)-oriented sapphire, and (111)-oriented perovskite-structured SrTiO3 and LaAlO3. Structural characterization confirms epitaxial growth with a (0001) out-of-plane orientation across all substrates. Synchrotron X-ray diffraction reveals that the films are highly relaxed, exhibiting systematic in-plane lattice variations driven by substrate-induced strain. Notably, films grown on perovskite substrates display enhanced in-plane crystal coherence compared to those on isostructural sapphire, indicating superior structural quality. These findings demonstrate the potential for seamless integration of hematite with perovskite oxides, enabling the development of high-quality oxide heterostructures for spintronic applications.