Modulated differential scanning calorimetry (MDSC) is right choice for measuring specific heat. Take a few measurements, then calculate stadard deviation and further calcualte relative standard error. If these values are less than 10%, we can say uncertainty is with the targetted values.
You can also compare the experimental value with theoretical or calculated or previously carried one. Otherwise, u recalibrate all the instruments and check the repeatability. See this value with in 1% error to get accurate experimental values.
You could also have a look at the supporting information of this article to see how the uncertainty has been calculated: Article Acoustic Method for Determination of the Thermal Properties ...
Its all in section B.PROPAGATION OF EXPERIMENTAL ERRORS.