Earth System Digital Twins (ESDTs) are emerging as a transformative paradigm for monitoring, forecasting, and managing complex systems through the integration of Earth observations, numerical simulations, artificial intelligence, and decision-support capabilities. Despite rapid advances in digital twin technologies, the systematic treatment of uncertainty remains a critical challenge that limits the reliability, interpretability, and operational adoption of ESDTs. This paper presents a comprehensive framework for uncertainty quantification (UQ) across the entire ESDT lifecycle, including observations, data fusion, model initialization, physical simulations, AI-driven predictions, scenario analyses, and decision-making processes. Drawing on representative case studies in air quality forecasting, wildfire prediction, flood modeling, water quality assessment, and satellite chlorophyll-a reconstruction, we identify major sources of uncertainty and evaluate methods for their characterization, propagation, validation, and communication. The framework integrates statistical, ensemble, physics-based, and machine-learning approaches to generate uncertainty-aware predictions and confidence measures. We further propose a maturity model and evaluation metrics for assessing uncertainty readiness in ESDTs. The resulting framework provides a foundation for developing trustworthy Earth system digital twins capable of supporting risk-informed environmental management, disaster response, and sustainability decision-making.