Abstract The traceback method allows the computation of the kinematic age of nearby young associations from astrometric and kinematic data alone, circumventing the need for stellar evolution models. Previous traceback age estimates have, however, often been incompatible with other age-dating methods. We apply the Kinematic Age for Nearby Young Associations traceback analysis tool on core samples, free of contaminants such as unresolved multiple systems, of carefully vetted members of the Tucana–Horologium (THA), Columba (COL), and Carina (CAR) associations, using data from Gaia Data Release 3 (DR3) data products and other kinematic surveys, in order to test whether the traceback method can be used successfully on 40–50 Myr old associations. Due to the lack of a clear boundary between members of COL and CAR, these two associations were combined in a single sample for the purpose of our analysis. Several systematic biases, including gravitational redshift, convective blueshift, and the bias on traceback ages due to random measurement errors, are accounted for. We find that the mean length of all branches between members and the trace of the ξ ′ η ′ ζ ′ spatial covariance matrix are the most robust and generalizable association size metrics among those that were tested. We obtain reliable constraints on the traceback ages: 44 . 8 − 7.0 + 2.1 Myr for THA, and 28 . 4 − 2.9 + 1.8 Myr for COL and CAR. These results are compatible with previous age estimates for THA, COL, and CAR computed with the isochrones and lithium depletion boundary methods.