We consider inverse problems of source identification in electroen-cephalography, modelled by elliptic partial differential equations. Being given boundary data that consist in values of the current flux and of the electric poten-tial on the scalp, the aim is to reconstruct unknown current sources supported within the brain. For spherical layered models of the head, and after a pre-liminary data transmission step, such inverse source problems are tackled using best rational approximation techniques on planar sections. Both theoretical and constructive aspects are described, while numerical illustrations are provided.