We describe what is to our knowledge the first nondestructive measurement of the evolution of an optical continuum as a function of distance along a nonlinear waveguide. Spectral mapping is achieved on a subwavelength scale by utilizing near-field microscopy to probe the waveguide's evanescent field. The measured continuum broadening along the waveguide agrees in general form with predictions of broadening from theoretical calculations, but differs in some important details. Subwavelength resolution measurements are made both along and across the waveguide to reveal spectral variations not seen before by other techniques.