A simulated amorphization and recrystallization strategy has been used to generate atomistic models of CaO and SrO nanoparticles, approximately 13 x 13 x 3 nm in size, supported on an MgO(001) substrate. The (single crystal) CaO nanoparticle exhibits a cubic "slab" morphology in contrast to the SrO nanoparticle, which has a convex-lens or "droplet" morphological appearance with a height of 3.5 nm and a diameter of about 14-15 nm. In addition, the SrO nanoparticle comprises 10 interconnecting misoriented crystallites. The epitaxial relationships that exist between the nanoparticle and substrate are identified and correlated with the lattice misfit together with the interfacial structures and complex dislocation networks that evolve within the nanoparticles. The atomistic structure of various screw-edge dislocation cores (in CaO), grain-boundaries, and grain-junctions (in SrO) that form within the nanoparticles are presented graphically. In addition, the structures of the nanoparticles are compared with previous simulations performed on the analogous CaO and SrO thin films supported on MgO(001).