Although orbital forcing is commonly proposed as the driver of ancient sedimentary rhythms, the lack of adequate independent time control (radio isotopic data) to calibrate these cycles has stood as a major challenge to evaluation of the hypothesis. Here I apply a new statistical approach to evaluate cyclicity in two historically important rhythmic units for which orbital forcing has been proposed: the Triassic Latemar Limestone (Dolomites, Italy) and the Eocene Green River Formation (Wyoming, USA). A major advance of the new method is its explicit evaluation of the null hypothesis of no orbital signal. The null hypothesis can be rejected with a high degree of confidence in the Latemar Limestone (probability <0.30%) and Green River Formation (probability <0.07%). The analyses also resolve controversies about the specific orbital calibrations at each site. Both data series reveal the expected precession, obliquity, and eccentricity orbital components, and yield astrochronologies that are consistent with proposed radio isotopic based time scales.