A system for passing an electromagnetic signal through a casing comprises a tool body that can be positioned inside the casing; means for magnetically saturating the casing in the vicinity of the tool; a transmitter for transmitting an electromagnetic signal from the tool antenna to the outside of the casing for reception at one or more sensors equipped with an antenna and electronic circuits located outside the casing; and a detector for detecting an electromagnetic signal at the tool from the sensor located outside the casing.