We examine the enhancement of optical trapping forces due to plasmon resonances of nanoshells. Nanoshells are nanoscale particles with a dielectric core and metallic coating that exhibit tunable plasmon resonances. Theory predicts that the optical trapping force may be three to fifty times larger for trapping-laser wavelengths near resonance than for wavelengths far from resonance . The resonance absorption of nanoshells can be tuned by adjusting the ratio of the radius of the dielectric core, r1, to the total radius, r2 . Using back focal plane detection, we measure the trap stiffness of optical tweezers, from lasers at 973 nm and 1064 nm, for single trapped nanoshells with several different r1/r2 ratios. Enhanced trapping strengths are not found through these measurements done with single wavelength optical traps. A tunable-wavelength laser trap will enable more conclusive results.