While general-purpose pTx coils mostly have identical elements arranged symmetrically, coils built for a specific application may be asymmetrical. This asymmetry may lead to a high variation in local SAR distributions of individual coil-elements. For an arterial spin labelling pTx coil, we show that using 2,000,000 unconstrained random excitations to characterize the maximum local-SAR underestimates the local-SAR by 7%. We also show that for the investigated ASL coil, the neck elements, which could be exclusively used for labelling, yield 33% less SAR than the head-imaging coils. Therefore, 50% higher power limits can be used for labelling part of an ASL sequence than the imaging part.