Spectrometer calibration accuracies are of high importance for a wide range of applications. Typically, one calibrates the spectrometer with a calibration lamp, providing distinct and well-defined calibration lines. However, for small spectral ranges, where only two calibration lines are present, the calibration becomes inaccurate. We present a high-precision nonlinear wavelength calibration method, which is based on two or more reference lines from a calibration lamp. The additional key element introduced is a Fabry-Perot multilayer structure that yields multiple sharp transmission maxima of similar intensity over the full spectrometer range under broad-band illumination (e.g., white-light source). An iterative algorithm is put forward to obtain a self-consistent calibration of picometer precision over the full spectrometer range. In regions distant from calibration lines the accuracy is enhanced by at least a factor of two compared to conventional methods.