The use of multiple substrates in color printers requires color characterization for each of the individual media. A full re-characterization for each substrate is measurement and labor intensive. In this paper, a variety of methods are proposed and evaluated for determining the color characterization for a new substrate based on a complete characterization on a reference substrate and a small number of additional measurements for the new substrate. This saves significant time and effort in comparison to the traditional method of repeating the color characterization for each new substrate. The methods developed and tested include model-based approaches based on Beer's law, Kubelka-Munk theory, and Neugebauer equations; and an empirical technique based on principal component analysis. Results indicate that the model based techniques offer only a small improvement over direct use of the reference characterization, whereas, the empirical technique offers a more significant improvement with as few as 16-26 measurements on the new substrate.