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The center-of-mass motion of optically trapped dielectric nanoparticles in a vacuum is extremely well decoupled from its environment, making a powerful tool for measurements of feeble subattonewton forces. We demonstrate a method to trap and maneuver nanoparticles in an optical standing wave potential formed by retroreflecting a laser beam from a metallic mirror surface. We can reliably position a $\sim <\#comment/>170\mathrm{n}\mathrm{m}$diameter silica nanoparticle at distances of a few hundred nanometers to tens of micrometers from the surface of a gold-coated silicon mirror by transferring it from a single-beam tweezer trap into the standing wave potential. We can further measure forces experienced by the particle while scanning the two-dimensional space parallel to the mirror surface, and we find no significant excess force noise in the vicinity of the surface. This method may enable three-dimensional scanning force sensing near surfaces using optically trapped nanoparticles, promising for high-sensitivity scanning force microscopy, tests of the Casimir effect, and tests of the gravitational inverse square law at micrometer scales.