The transport of passive tracers observed by the Upper Atmosphere Research Satellite is simulated using computed three-dimensional trajectories of ≈ 100 000 air parcels initialized on a stratosphere grid, with horizontal winds provided by the United Kingdom Meteorological Office data assimilation system, and vertical (cross isentropic) velocities computed using a fast radiation code. The conservative evolution of trace constituent fields is estimated over 20–30-day periods by assigning to each parcel the observed mixing ratio of the long-lived trace gases N20 and CH4 observed by the Cryogenic Limb Army Etalon Spectrometer (CLAES) and H2O observed by the Microwave Limb Sounder (MLS) on the initialization date. Agreement between calculated and observed fields is best inside the polar vortex and is better in the Arctic than in the Antarctic. Although there is not always detailed agreement outside the vortex, the trajectory calculations still reproduce the average large-scale characteristics of passive tracer evolution in midlatitudes. In late winter, synoptic maps from trajectory calculations reproduce all major features of the observations, including large tongues or blobs of material drawn from low latitudes into the region of the anticyclone during February–March 1993. Comparison of lower-stratospheric observations of the CLAES tracers with the calculations suggests that discontinuities seen in CLAES data in the Antarctic late winter lower stratosphere are inconsistent with passive tracer behavior. In the Arctic, and in the Antarctic late winter, MLS H20 observations show behavior that is inconsistent with calculations and with that expected for passive tracers inside the polar vortex in the middle-to-upper stratosphere. Diabatic descent rates in the Arctic lower stratosphere deduced from data are consistent with those from the calculations. In the Antarctic lower stratosphere, the calculations appear to underestimate the diabatic descent. The agreement between large-scale features of calculated and observed tracer fields supports the utility of these calculations in diagnosing trace species transport in the winter polar vortex.