Chromatic dispersion of a 37 cm long, solid-core photonic bandgap (PBG) fiber was studied in the wavelength range of 740-840 nm with spectral interferometry employing a Mach-Zehnder interferometer and a high resolution spectrometer. The interferometer was illuminated by a Ti:sapphire laser providing 20 fs pulses. A comparative study has been carried out to find the most accurate spectral phase retrieval method that is suitable for measuring higher order chromatic dispersion. The stationary phase point, the minima-maxima, the cosine function fit, the Fourier transform, and the windowed Fourier transform methods were tested. It was shown that out of these five techniques, the Fourier-transform method provided the dispersion coefficients with the highest accuracy, and it could also detect rapid phase changes in the vicinity of leaking mode frequencies within the transmission band of the PBG fiber.