Deep learning appearance-based 3D gaze estimation is gaining popularity due to its minimal hardware requirements and being free of constraint. Unreliable and overconfident inferences, however, still limit the adoption of this gaze estimation method. To address the unreliable and overconfident issues, we introduce a confidence-aware model that predicts uncertainties together with gaze angle estimations. We also introduce a novel effectiveness evaluation method based on the causality between eye feature degradation and the rise in inference uncertainty to assess the uncertainty estimation. Our confidence-aware model demonstrates reliable uncertainty estimations while providing angular estimation accuracies on par with the state-of-the-art. Compared with the existing statistical uncertainty-angular-error evaluation metric, the proposed effectiveness evaluation approach can more effectively judge inferred uncertainties' performance at each prediction.