Graphene transfer onto ceramics, like Si/SiO2, is well-developed and described in the literature. However, it is problematic for other ceramic materials (e.g., Al2O3 and ZrO2), especially porous ones. In this case, it is mainly due to poor adhesion to the substrate, resulting in strong degradation of the graphene. For these reasons, the research topic of this study was undertaken. This article presents research on the development of the methodology of graphene transfer onto ceramic Al2O3 surfaces. Polycrystalline graphene chemical vapour deposition (CVD) monolayer and quasimonocrystalline high-strength metallurgical graphene (HSMG®) synthesised on liquid copper were used. When developing the transfer methodology, the focus was on solving the problem of graphene adhesion to the surface of this type of ceramic, and thus reducing the degree of graphene deterioration at the stage of producing a ceramic–graphene composite, which stands in the way of its practical use. Plasma and chemical ceramic surface modification were applied to change its hydrophobicity, and thus to improve the adhesion between the graphene and ceramic. The modification included the use of dielectric barrier discharge (DBD) plasma, oxygen plasma (RF PACVD method - Radio Frequency Plasma Assisted Chemical Vapour Deposition), and hydrofluoric acid treatment. Changes in surface properties caused by the modifications were determined by measuring the contact angle and (in the case of chemical modification) measuring the degree of surface development. The effectiveness of the applied surface preparation methodology was evaluated based on the damage degree of CVD and HSMG® graphene layer transferred onto modified Al2O3 using optical microscopy and Raman spectroscopy. The best average ID/IG ratio for the transferred HSMG® graphene was obtained after oxygen plasma modification (0.63 ± 0.18) and for CVD, graphene DBD plasma was the most appropriate method (0.17 ± 0.09). The total area of graphene defects after transfer to Al2O3 was the smallest for HSMG® graphene after modification with O2 plasma (0.251 mm2/cm2), and for CVD graphene after surface modification with DBD plasma (0.083 mm2/cm2).