We report a general chemical strategy for producing reduced-symmetry metallodielectric nanoparticles, nanocups, and nanocaps that combines nanoscale masking techniques and nanoparticle-seeded electroless plating. Using this approach, silica nanoparticles with a gold cup-shaped shell and, alternatively, a gold cap, are obtained. The plasmon response of both nanostructures is a sensitive function of orientation of the nanostructure with respect to the direction and polarization of incident light. This orientation dependence is examined experimentally by studying the extinction spectra of oriented nanocups and nanocaps on transparent substrates, and is also evaluated theoretically using a three-dimensional finite difference time domain (FDTD) method.