In the KATRIN neutrino mass experiment, radioactive decays inside the large UHV chamber of the Main Spectrometer can increase the background rate considerably and thus, diminish the sensitivity for the actual signal. In particular, the amount of the short-lived radon isotopes R219n and R220n has to be reduced. Three LN2 -cooled cryogenic baffles have been installed to capture the radon atoms before they decay. However, radon does not stick to a cold surface indefinitely. It either desorbs after a limited sojourn time, or it decays into polonium.We compare two different methods which describe the radon suppression for different baffle temperatures. The first method calculates the suppression factor analytically, using the effective pumping speed and the transmission probability of the baffles simulated with the Test Particle Monte Carlo code MolFlow+. A newly introduced effective sticking coefficient takes into account the radon lifetime and its mean sojourn time on the cold copper baffles. For the second method the MolFlow+ code was extended to simulate directly the radon lifetime and sojourn time. At the end experimental data are compared to the simulations and the mean sojourn time is determined as a function of the baffle temperature.