We show how a combination of near-field scanning optical microscopy with crossed beam spectral interferometry allows a local measurement of the spectral phase and amplitude of light propagating in photonic structures. The method only requires measurement at the single point of interest and at a reference point, to correct for the relative phase of the interferometer branches, to retrieve the dispersion properties of the sample. Furthermore, since the measurement is performed in the spectral domain, the spectral phase and amplitude could be retrieved from a single camera frame, here in 70 ms for a signal power of less than 100 pW limited by the dynamic range of the 8-bit camera. The method is substantially faster than most previous time-resolved NSOM methods that are based on time-domain interferometry, which also reduced problems with drift. We demonstrate how the method can be used to measure the refractive index and group velocity in a waveguide structure.