Accurate estimation of brain age from MRI morphological features is essential for understanding neurodevelopmental processes and aging trajectories. Moreover, deviations between estimated brain age and chronological age may serve as indicators of accelerated/decelerated aging processes associated with neurological conditions. This study proposes a novel framework for brain age prediction using Machine Learning (ML), specifically Random Forests Regression (RFR) and Quantile Regression (RFQR), integrated - for the first time - with conformal prediction through Model Agnostic Prediction Interval Estimator (MAPIE), to construct statistically rigorous prediction intervals and to quantify uncertainty while maintaining coverage guarantee. Models were trained on FreeSurfer morphometrics of HCP Young Adult (754 individuals, age 22–36). RFR and RFQR achieved similar MAE (2.8) for mean and median prediction, whereas RFQR had higher MAE values (5.83 and 5.37) for lower and upper quantile predictions. Feature importance revealed that the thickness of left caudal and right rostral middle frontal cortices, along with the volume of right putamen, were the most important variables in all models. MAPIE found that RFR exhibited an average prediction interval width of 10.2 years with 89% coverage, while RFQR had higher coverage of 98% with a slightly wider width (11.17), thus surpassing the desired 90% coverage. In conclusion, our study demonstrates that RFQR, utilizing conformalized quantile regression, produces robust brain age prediction intervals with high coverage using structural MRI features in young healthy controls. Our findings encourage the application of such novel framework for the early detection of neurological disorders, as well as for enhancing personalized medicine.