Optical channel monitors (OCMs) that use scanning filters need to resolve the amplified spontaneous emission (ASE) noise floor between channels in order to determine optical signal-to-noise ratio (OSNR). We show how regularized least-squares can extract accurate OSNR values from raw spectra when the ASE floor is not visible because of insufficient resolution in the monitor. Our experimental results demonstrate OSNR measurement accuracy to within 0.6 dB from a spectrum of 50-GHz-spaced 10-Gb/s channels measured using a scanning Fabry-Peacuterot filter with 35-GHz bandwidth. The ability to use broader bandwidth filters in OCMs without sacrificing accuracy may reduce their cost and increase their robustness