Geometry calculations were performed on pure BaCeO3 fragments and on Y-and In-doped derivatives. HF and DFT approaches were used to investigate monoclinic and orthorhombic structures. The Computational methods, structural models, and electronic structure investigation protocols were tuned taking into consideration and balancing the consistency of the results against the computational cost. The calculated structures and energetics parameter, as well as the detailed orbital analysis performed on the corresponding BaCeO3 derivatives allowed us to explain experimental findings and to develop a procedure to study the cationic octahedral environment of doped X:BaCeO3 (X = Y, In) and undoped BaCeO3 protonic conductors useful to interpret experimental results and hopefully to design new experimental approaches. In detail, distances and angles of the studied materials are easily captured in the frame of the HF paradigm even by using low-level ECP basis sets. While, pure electronic-based approaches, involving the investigation of the Partial Density of States resulting from the C-Squared Population Analysis, show that the dopant species must leave unchanged, or even decrease, the local basicity of the oxygen octahedral environment in order to increase the conductivity of the BaCeO3 derivatives. Whereas local structural changes that are not related to the basicity above affect to a less, if not null, extent the conductivity of the same derivatives.