To improve the limit of detection in a nanoplasmonic sensor system, the optical performance of the metal nanostructures should be optimized according to the best spectral window of the measurement instrument. We propose that the spectral window from 1460 to 1610 nm can potentially provide ultrahigh instrumental resolution for biosensing. We optimized gold nanoring arrays such that the extinction peak position is inside the proposed window, the extinction peak is sharp enough to track the peak shift with high resolution and the figure of merit (sensitivity/linewidth) of the array is optimized at the same time. The peak-sharpening effect of the array caused by coherent interaction plays a central role in the optimization. The optimized array has a lattice constant in the range [1000 nm,1060 nm], a bulk index sensitivity of around 450 nm/RIU and a figure of merit larger than 4. It is an enabling sensor element for a near-infrared sensor chip with ultrahigh resolution.