We report a study of the wetting and ordering of thermotropic liquid crystal (LC) droplets that are trapped (or "caged") within micrometer-sized cationic polymeric microcapsules dispersed in aqueous solutions of surfactants. When they were initially dispersed in water, we observed caged, nearly spherical droplets of E7, a nematic LC mixture, to occupy similar to 40% of the interior volume of the polymeric capsules [diameter of 6.7 +/- 0.3 mu m, formed via covalent layer-by-layer assembly of branched polyethylenimine and poly(2-vinyl-4,4-dimethylazlactone)] and to contact the interior surface of the capsule wall at an angle of similar to 157 +/- 11 degrees. The internal ordering of LC within the droplets corresponded to the so-called bipolar configuration (distorted by contact with the capsule walls). While the effects of dodecyltrimethylammonium bromide (DTAB) and sodium dodecyl sulfate (SDS) on the internal ordering of "free" LC droplets are similar, we observed the two surfactants to trigger strikingly different wetting and configurational transitions when LC droplets were caged within polymeric capsules. Specifically, upon addition of SDS to the aqueous phase, we observed the contact angles (theta) of caged LC on the interior surface of the capsule to decrease, resulting in a progression of complex droplet shapes, including lenses (theta approximate to 130 +/- 10 degrees), hemispheres (theta approximate to 89 +/- 5 degrees), and concave hemispheres (theta < 85 degrees The wetting transitions induced by SDS also resulted in changes in the internal ordering of the LC to yield states topologically equivalent to axial and radial configurations. Although topologically equivalent to free droplets, the contributions that surface anchoring, LC elasticity, and topological defects make to the free energy of caged LC droplets differ from those of free droplets. Overall, these results and others reported herein lead us to conclude that caged LC droplets offer a platform for new designs of LC-droplet-based responsive soft matter that cannot be realized in dispersions of free droplets.