In this paper two typical arrangements of underground single-core high voltage three-phase power cables (flat and trefoil protected by PVC pipes) inside a closed shield of three different materials (low-carbon steel, non-oriented grain steel and aluminium) are analysed. The shield has two components: a U-shaped base and a flat plate (cover) located on top of the base. Whereas most of previous papers on this subject only dealt with the degree of mitigation obtained with each material, this paper, in addition to also addressing this issue, mainly focusses on the effect that electromagnetic losses induced in the shield have on the ampacity of the cable and the cost involved (material and losses). To obtain the numerical results, a high number of simulations by a well-known commercial finite element method software (COMSOL Multiphysics) have been performed. The results obtained in the numerous cases analysed are widely commented and the solutions that enable an important mitigation with no current derating and at a comparatively low cost are highlighted.