We study the collimation of relativistic magnetohydrodynamic jets by the pressure of an ambient medium, in the limit where the jet interior loses causal contact with its surroundings. This follows up a hydrodynamic study in a previous paper, adding the effects of a toroidal magnetic field threading the jet. As the ultrarelativistic jet encounters an ambient medium with a pressure profile with a radial scaling of p ∝ r−η where 2 < η < 4, it loses causal contact with its surroundings and forms a boundary layer with a large pressure gradient. By constructing self-similar solutions to the fluid equations within this boundary layer, we examine the structure of this layer as a function of the external pressure profile. We show that the boundary layer always becomes magnetically dominated far from the source, and that in the magnetic limit, physical self-similar solutions are admitted in which the total pressure within the layer decreases linearly with distance from the contact discontinuity inwards. These solutions suggest a ‘hollow-cone’ behaviour of the jet, with the boundary-layer thickness prescribed by the value of η. In contrast to the hydrodynamical case, however, the boundary layer contains an asymptotically vanishing fraction of the jet energy flux.