We explore the influence of the metal microstructure on the compressive flow stress of replicated microcellular 400-mu m pore size Al-4.5 wt%Cu solidified at two different solidification cooling rates, in the as-cast and T6 conditions. It is found that the yield strength roughly doubles with age-hardening, but does not depend on the solidification cooling rate. Internal damage accumulation, measured by monitoring the rate of stiffness loss with strain, is similar across the four microstructures explored and equals that measured in similar microcellular pure aluminium. In situ flow curves of the metal within the open-pore microcellular material are back-calculated using the Variational Estimate of Ponte-Castaeda and Suquet. Consistent results are obtained with heat-treated microcellular Al-4.5 wt%Cu and are also obtained with separate data for pure Al; however, for the as-cast microcellular Al-4.5 wt%Cu, the back-calculated in situ metal flow stress decreases, for both solidification rates, with decreasing relative density of the foam. We attribute this effect to an interplay between the microstructural and mesostructural features of the microcellular material: variations in the latter with the former held constant can alter the scaling between flow stress and relative density within microcellular alloys.