Single, microscopic, aqueous solution droplets of NaCl, CsCl, KF, and NaNO3 are levitated in a quadrupole trap filled with water vapor at room temperature. The solutions become supersaturated as the pressure of the vapor is slowly reduced until solidification occurs. Both homogeneous droplets and those consisting of a solution jacket surrounding a solid core of a similar salt, KCl for the first three, Na2SO4 for the last, are studied. Except for KF, the solid catalyzes the nucleation, reducing the maximum supersaturation to 48, 78, and 64% of its value in the absence of the solid for the other three, respectively. Classical nucleation theory yields the critical size of the nucleus, its surface energy density, and, assuming it is a spherical cap on the surface of the solid core, the wetting angle.