The aim of this study is to propose a test method for the determination of the quality of transformer paper insulation. For this purpose, the oil/cellulose insulation systems were exposed to various accelerated aging tests. The results of the aging experiments of normal Kraft and thermally upgraded papers, two different types of transformer oil (mineral and natural ester), and copper are shown. Aging was carried out in various experiments at 150 °C, 160 °C, 170 °C, and 180 °C with dry (initial values ≤ 0.5%) and moistened cellulose insulation (initial values 3–3.5%). Following insulating oil and paper, degradation markers were measured: the degree of polymerization, tensile strength, furan derivates, methanol/ethanol, acidity, interfacial tension, and dissipation factor. It was found that the aging of cellulose insulation in cycles was 1.5–1.6 times faster in comparison to continuous aging, due to the more pronounced effect of hydrolytic mechanism in cyclic aging owing to the produced and absorbed water. Furthermore, it was observed that the high initial water content in cellulose increases the aging rate two to three times more than in the dry experimental setup. The proposed aging test in cycles can be used to achieve faster aging and to compare the quality of different insulating papers.