One of the consequences of antisymmetric spin–orbit interactions due to a lack of inversion symmetry are unusually large upper critical fields observed in heavy-electron superconductors. The upper critical fields of non-centrosymmetric CeRhSi3 and CeIrSi3 cannot be explained by the BCS theory. In order to elucidate the mechanism of the anomalous upper critical fields of superconductivity, we have performed inelastic neutron scattering experiments using polycrystalline samples of CeRhSi3 and CeIrSi3 to determine the crystalline electric field level scheme. The crystalline electric field excitations of CeRhSi3 and CeIrSi3 were observed at around 19, 35 and 24, 41 meV, respectively. In this paper, we categorize the physical properties of the CeTX3 system and discuss the mechanism of anomalous superconductivity and the influence of f-electrons.