Field induced structural (Freedericksz) transitions in supramicron nematic and cholesteric liquid crystal droplets embedded in a solid matrix are theoretically analysed. Taking into account the elastic, surface, and field free energy contributions, the equilibrium structures and phase diagrams are obtained. The predicted strong dependence of the radial - axial structural transition on the value of the saddlesplay splay elastic constant K24is proposed to be used for the indirect determination of this constant.