I have fitted some data using the convoluted landau and gaussian routine from root.cern.ch/root/html/tutorials … aus.C.html, and I want the most probable value of the distribution. So I search for the maximum value of the landau-gaussian convoluted function, but I was wondering if there is some way of finding the error of that maximum value. Does root save errors for each fit value as a function of x, or will I have to estimate it in some way?

I guess you will have to estimate that error someway. You have errors on the distribution parameter coming from the fit and then if you have an analytical formula for the maximum, you could use error propagation.
If you don;t have any analytical formula, then you should use a bootstrap procedure, running toy pseudo-experiments, to estimate this error.
Keep in mind also that the convolution performed in the tutorial is an approximation, and can also have an error. You might try to use numerical integral or fft to do the convolution.
Then once you have the fitted function you can use TF1::GetMaximum to get its mode