The peak location of the localized surface plasmon resonance (LSPR) of noble metal nanoparticles is highly dependent upon the refractive index of the nanoparticles' surrounding environment. In this study, new phenomena are revealed by exploring the influence of interacting molecular resonances and nanoparticle resonances. The LSPR peak shift and line shape induced by a resonant molecule vary with wavelength. In most instances, the oscillatory dependence of the peak shift on wavelength tracks with the wavelength dependence of the real part of the refractive index, as determined by a Kramers-Kronig transformation of the molecular resonance absorption spectrum. A quantitative assessment of this shift based on discrete dipole approximation calculations shows that the Kramers-Kronig index must be scaled in order to match experiment.