We introduce a probabilistic approach for dating historical manuscript pages from visual features alone. Instead of aggregating centuries into classes as is standard in the previous literature, we pose dating as an evidential deep regression problem over a continuous year axis, allowing our neural network to output a full predictive distribution with decomposed aleatoric and epistemic uncertainty in a single forward pass. Our architecture combines an EfficientNet-B2 backbone with a Normal-Inverse-Gamma (NIG) output head trained with a joint negative-log-likelihood and evidence-regularization objective. On the DIVA-HisDB benchmark (150 pages, 3 medieval codices, 151,936 patches), our model scores a test MAE of 5.4 years, well below the 50-year century-label supervision granularity, with 93\% of patches within 5 years and 97\% within 10 years. Our approach achieves \textbf{PICP=92.6\%}, the best calibration among all compared methods, in a single forward pass, outperforming MC Dropout (PICP=88.2\%, 50 passes) and Deep Ensembles (PICP=79.7\%, 5 models) at $5\times$ lower inference cost. Uncertainty decomposition shows aleatoric uncertainty is a strong predictor of dating error (Spearman $ρ=0.729$), and a selective prediction about the most certain 20\% of patches can provide \textbf{0.5 years MAE}. We show that predicted uncertainty increases as image degradation worsens, spatial decomposition maps explain which script regions cause aleatoric uncertainty, and page-level aggregation reduces MAE to 4.5 years with $ρ=0.905$ between uncertainty and page-level error.