Second-harmonic generation of blue light in quasi-phase-matching waveguides is analyzed with respect to the linewidth of the pump radiation. From the coupled-wave equation, when the pump linewidth is small, the conversion efficiency is shown to be enhanced by a factor of 2, compared with a single-mode case. A degradation of 3 dB occurs for a linewidth of three times the acceptance bandwidth. We also analyze the influence of the pump spectrum on measurements when the frequency response of a waveguide is evaluated by tuning the fundamental wavelength or by measuring the spectrum of the generated second-harmonic radiation.