Optical trapping forces are dependent upon the difference between the trap wavelength and the extinction (scattering plus absorption) resonances of a trapped particle. This leads to a wavelength-dependent trapping force, which should allow for the optimization of optical tweezers systems, simply by choosing the best trapping wavelength for a given experiment. Although optical forces due to a near-resonant laser beam have been extensively studied for atoms, the situation for larger particles has not been explored experimentally. The ability to selectively trap certain particles with a given extinction peak may have many practical applications. Here, resonance-based trapping is investigated using nanoshells, particles with a dielectric core and metallic coating that exhibit tunable plasmon resonances, and with silica and polystyrene beads. A measure of the trap strength was realized for single particles trapped in three dimensions, and near-resonant trapping was investigated by measuring the trap strength as a function of trap wavelength. Since the resulting trapping is highly temperature dependent, this necessitated temperature measurements of single optically trapped particles. To make these measurements a new optical tweezer apparatus was designed and constructed; the apparatus has wavelength tunability and was used to study these resonance effects. Optical trap stiffness, which is analogous to the spring constant of a stable trap, is measured for trapped particles that exhibit either single or multiple extinction resonances. The applications of this apparatus are not limited to force spectroscopy. Other measurement systems and techniques could be easily implemented into the custom-built apparatus, allowing for the measurement of various properties of single optically trapped particles as a function of wavelength.