We explore the influence of the metal microstructure on the compressive flow stress of replicated microcellular 400 µm pore size Al-4.5wt%Cu solidified at two different solidification cooling rates, in 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 Castañeda and Suquet. Consistent results are obtained with heat-treated microcellular Al-4.5wt%Cu, and are also obtained with separate data for pure Al; however, for as-cast microcellular Al-4.5wt%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 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.