Nanoparticles of NaGdF4 doped with trivalent erbium (Er3+) and ytterbium (Yb3+) are prepared by a modified thermal decomposition synthesis from trifluoroacetate precursors in 1-octadecene and oleic acid. The nanoparticles emit visible upconverted luminescence on excitation with near-infrared light. To minimize quenching of this luminescence by surface defects and surface-associated ligands, the nanoparticles are coated with a shell of NaGdF4. The intensity of the upconversion luminescence is compared for nanoparticles that were coated with an undoped shell (inert shell) and similar particles coated with a Yb3+-doped shell (active shell). Luminescence is also measured for nanoparticles lacking the shell (core only), and doped with Yb3+ at levels corresponding to the doped and undoped core/shell materials respectively. Upconversion luminescence was more intense for the core/shell materials than for the uncoated nanoparticles, and is greatest for the materials having the "active" doped shell. Increasing the Yb3+ concentration in the "core-only" nanoparticles decreases the upconversion luminescence intensity. The processes responsible for the upconversion are presented and the potential advantages of "active-core"/"active-shell" nanoparticles are discussed.