Frequency doubling of an infrared laser radiation in non-linear optical crystals is a widely used technique to obtain light in the visible range. The second harmonic generation process is influenced by several well-known parameters. In this article we study the effect of group delay dispersion on the second harmonic generation process for femtosecond pulses. We show, both through simulation and experiments, that for certain parameters even a small amount of chirp can have a detrimental effect on the conversion efficiency as well as the second harmonic beam quality. We also check the effect of higher order dispersion. By properly accounting for those effects the crystal length and focusing conditions can be optimized to reach high conversion efficiency, while maintaining low sensitivity to chirp variations and good beam quality.