Recent works in the development of nanostructured catalysts for bromate reduction in drinking water under hydrogen have highlighted the importance of the properties of the metallic phase support in their overall performance. Since most works in catalyst development are carried out in powder form, there is an overlooked gap in the correlation between catalyst support properties and performance in typical continuous applications such as fixed bed reactors. In this work, it is shown that the mechanical modification of commercially available carbon nanotubes, one of the most promising supports, can significantly enhance the activity of the catalytic system when tested in a stirred tank reactor, but upon transition to a fixed bed reactor, the formation of preferential pathways for the liquid flow and high pressure drops were observed. This effect could be minimized by the addition of an inert filler to increase the bed porosity; however, the improvement in catalytic performance when compared with the as-received support material was not retained. The operation of the continuous catalytic system was then optimized using a 1 wt.% Pd catalyst supported on the as-received carbon nanotubes. Effluent and hydrogen flow rates as well as catalyst loadings were systematically optimized to find an efficient set of parameters for the operation of the system, regarding its catalytic performance, capacity to treat large effluent flows, and minimization of catalyst and hydrogen requirements. Experiments carried out in the presence of distilled water as a reaction medium demonstrate that bromate can be efficiently removed from the liquid phase, whereas when using a real water matrix, a tendency for the deactivation of the catalyst over time was more apparent throughout 200 flow passages over the catalytic bed, which was mostly attributed to the competitive adsorption of inorganic matter on the catalyst active centers, or the formation of mineral deposits blocking access to the catalyst.