Multiwalled carbon nanotubes have outstanding mechanical properties that, when combined with Portland cement, can provide cementitious composites that could lead to the innovative construction of stronger, lighter, and thinner built infrastructure. This paper addresses a knowledge gap that relates to the durability of CNT–cement composites. The durability to corrosive chloride, uptake of water by sorption, and flow of the permeability of water acting under high water pressure are addressed. Flow simulations were undertaken through segmented 3D pore networks, based on X-ray computed microtomography measurements, the creation of a virtual microstructure, and fluid simulations that were compared with larger-scale samples. The investigation showed decreased water sorptivity of CNT–cement mixtures, indicating improved durability for the cover zone of concrete that is prone to the uptake of water and water-borne corrosives. Chloride diffusion of CNT–cement composites provided up to 63% improvement compared with control samples. The favourable durability bodes well for the construction of long-life CNT-reinforced concrete infrastructure.