Accurate age-depth models for proxy records are crucial for inferring changes to the environment through space and time, yet traditional methods of constructing these models assume unrealistically small age uncertainties and do not account for many geologic complexities. Here we modify an existing Bayesian age-depth model to foster its application for deep time U-Pb and 40Ar/39Ar geochronology. More flexible input likelihood functions and use of an adaptive proposal algorithm in the Markov Chain Monte Carlo engine better account for the age variability often observed in magmatic crystal populations, whose dispersion can reflect inheritance, crystal residence times and daughter isotope loss. We illustrate this approach by calculating an age-depth model with a contiguous and realistic uncertainty envelope for the Miocene Santa Cruz Formation (early Miocene; Burdigalian), Argentina. The model is calibrated using new, high-precision isotope dilution U-Pb zircon ages for stratigraphically located interbedded tuffs, whose weighted mean ages range from ca. 16.78 ± 0.03 Ma to 17.62 ± 0.03 Ma. We document how the Bayesian age-depth model objectively reallocates probability across the posterior ages of dated horizons, and thus produces better estimates of relative ages among strata and variations in sedimentation rate. We also present a simple method to propagate age-depth model uncertainties onto stratigraphic proxy data using a Monte Carlo technique. This approach allows us to estimate robust uncertainties on isotope composition through time, important for comparisons of terrestrial systems to other proxy records.