In the accelerated development pipeline of sustainable materials with tailored properties for superior performance, data-driven surrogate models play a vital role in modelling the process-structure-property (PSP) linkage. Deep learning (DL) models are applied for regression tasks due to their accurate point predictions, which are oftentimes overconfident and lacking regarding the quantity, coverage and type of uncertainties. This deters the use of DL models in inverse design, alongside their integration with active learning to explore the material design space. To address this gap, uncertainty quantification (UQ) methods are utilized to deliver comprehensive information about model accuracies and uncertainties. UQ frameworks such as Bayesian Neural Network (BNN), Conformal Predictor (CP) and Conformalized Quantile Regression (CQR) are investigated. BNNs are neural networks incorporated with Bayesian inference [2], while CPs are wrapper frameworks that generate statistically guaranteed, distribution-free intervals [3]. CQRs combine quantile regression and CP to provide regression output intervals with calibrated and statistically guaranteed coverage [4]. Case studies with datasets of known structure-property relations, based on the Ising model and Cahn-Hilliard equations, compared to a ResNet18 base architecture [5] shows that both BNN and CQR capture input-dependent model and data uncertainties with well-calibrated prediction intervals. The combination of CP with ResNet18 delivers comparable point-prediction accuracy as aformentioned frameworks with prediction intervals of consistent empirical coverage, but is limited to the quantification of the model uncertainty. These findings depict the robustness of UQ-equipped DL models in turning black-box surrogate models for into uncertainty-aware frameworks. For forward PSP relation modelling, this ensures realibility when extrapolating beyond the sparse dataset. When combined with active learning algorithms with Bayesian optimisation, knowledge-based exploration of the vast material design space enables a closed-loop material discovery pipeline for inverse design. While benchmarked on simulated microstructural data, this approach is transferable to real experimental datasets.