Inspired by a paper by T. Chakradhar, K. Gittins, G. Habib and N. Peyerimhoff, we analyze their conjecture that the ground state energy of the magnetic Dirichlet-to-Neumann operator tends to + infinity as the magnetic field tends to + infinity. More precisely, we explore refined conjectures for general domains in the plane based on the previous analysis in the case of the half-plane and the disk by Helffer-Nicoleau. This is a work in collaboration with Ayman Kachmar and François Nicoleau.