We show high resolution measurements of a surface plasmon resonance (SPR) sensor based on a rectangular nanohole array in a metal film. This SPR setup uses balanced intensity detection between two orthogonal polarizations of a He-Ne laser beam, which allows for sensitivity improvement, noise reduction and rejection of any uncorrelated variation in the intensity signal. A bulk sensitivity resolution of 6.4 x 10(-6) RIU is demonstrated. The proposed methodology is promising for applications in portable nanoplasmonic multisensing and imaging.