SiC and Ga2O3 are promising wide band gap semiconductors for applications in power electronics because of their high breakdown electric field and normally off operation. However, lack of a suitable dielectric material that can provide high interfacial quality remains a problem. This can potentially lead to high leakage current and conducting loss. In this work, we present a novel atomic layer deposition process to grow epitaxially MgxCa1−xO dielectric layers on 4H-SiC(0001) and β-Ga2O3$\left( {\bar 201} \right)$ substrates. By tuning the composition of MgxCa1−xO toward the substrate lattice constant, better interfacial epitaxy can be achieved. The interfacial and epitaxy qualities were investigated and confirmed by cross-sectional transmission electron microscopy and X-ray diffraction studies. Mg0.72Ca0.28O film showed the highest epitaxy quality on 4H-SiC(0001) because of its closest lattice match with the substrate. Meanwhile, highly textured Mg0.25Ca0.75O films can be grown on β-Ga2O3$\left( {\bar 201} \right)$ with a preferred orientation of (111).