The techniques of electromagnetic levitation, drop-tube processing and atomization are used to study containerless solidification of the Cu-Ni and Fe-Ni systems. Microstructure-selection maps are developed for the case of droplet solidification where droplet diameter and undercooling are the process parameters. The microstructure varies systematically with undercooling and composition, such that grain-refined microstructures are produced at both low and high undercoolings and dendritic microstructures are produced at intermediate undercoolings. The results are analyzed within a recently developed model for grain refinement which is based on the fragmentation of primary dendrites. The role of cooling rate in determining whether the microstructure transforms in the solid state or is retained as a primary structure is explored.