Currently, I am doing a lab in school on atomic spectroscopy. After taking readings of strong emission lines of various elements, I have fit the data using a Voigt Profile function from lmfit. The function minimizes the reduced chi-squared and returns the best fit along with fitting parameter values (center, amplitude, sigma, gamma). I am mainly interested in the center of the line profile. But, what is the uncertainty in this reported center? Or how would I report the measurement and its uncertainty.
If you are doing chi-squared fitting, then a value for the uncertainty (or an estimate) should have been returned by the software. If not, you could perhaps manually estimate by fixing the line centre at various values, allowing the other parameters to be fitted, and seeing where the minimum chi-squared increases by 1 over the global minimum.
Failing that, output your spectrum as an ASCII file and fit it with something that does provide uncertainties like gnuplot.
Failing that, here's a rule of thumb. The line centre is determined with a precision given by the FWHM divided by the signal to noise ratio per pixel.
Note that none of the above take any account of uncertainties in the wavelength calibration.
EDIT: It appears that lmfit does estimate uncertainties. https://lmfit.github.io/lmfit-py/confidence.html