You're looking for the error in the linewidth or integral? Each peak has its own width/integral, so I'm not sure what you'd be looking for...n=1 for each peak, and a standard error wouldn't be defined. I think the systematic error in those fits is fairly low if the digital resolution is high enough (like lots of zero filling) and wouldn't be appropriate as an overall measure of uncertainty. I've attached a link with some good references. 

For an n=1 parameter estimation problem, Bayesian approaches are attractive. I also added a link to an appropriate software passage, but it looks a little out of date. Still the description seems fitting:

The Errors in Variables package solves the errors in variables problem. In this problem one has a data set that has uncertainty in both the X and Y variables. These errors may be know or unknown, so this package solves four different errors in variables problems. 

http://www.umich.edu/~chemnmr/docs/Quantitative_NMR.pdf

http://bayesiananalysis.wustl.edu/

I agree with Ryan, didn't comprehend what you are looking for! for a standard deviation for anything to be obtained n should be more than 1

One possible way is to apply a mixed gaussian/lorentzian lineshape fit to the peaks (works pretty well), this can be done in TopSpin, I'm not sure about Mestrec. The TopSpin fit procedure will provide you with error values, and probably the integrals will even be included ther. Why do you need an error estimation for your integrals? The problem here is that the error will not only depend on the "mathematical fitting" to the peak shape - processing procedures for the spectrm will be the dominant influence here. I should guess that the actual errors in the integrals will be small...

I have quite long experimental times per spectrum. That is the reason I am tied to n =1. Yeah, you are right, I will probably miss random/systematic errors due to processing or experimental setup. So I thought I should at least account for the random errors due to the SNR in the spectrum.

I am performing a lineshape analysis to obtain koff for a protein-ligand system.

In the end, I exported the processed spectra to Origin and used a lorentzian lineshape fit. Works pretty well and the errors I obtain from the fitting procedure are definietly helpful to judge whether deviations in the lineshape analysis/affinity determination can be explained by the SNR.