Unlike statistical errors, whose importance has been well established in astronomical applications, uncertainties in instrument calibration are generally ignored. Despite wide recognition that uncertainties in calibration can cause large systematic errors, robust and principled methods to account for them have not been developed, and consequently there is no mechanism by which they can be incorporated into standard astronomical data analysis. Here we present a framework where they can be encoded such that they can be brought within the scope of analysis. We describe this framework, which is based on a modified MCMC algorithm, and propose a format standard derived from experience with effective area measurements of the ACIS-S detector on Chandra that can be applied to any instrument or method of codifying systematic errors. Calibration uncertainties can then be propagated into model parameter estimates to produce error bars that include systematic error information.