Binary classifications are commonly used in modeling continuously evolving systems, known as dynamic systems, especially in machine learning and deep learning applications. This is because the model's predictions are tied to real-world decisions. This thesis proposes a framework to enhance the trustworthiness of such binary classifications under various sources of uncertainty, focusing on malware detection and wildfire prediction. In these contexts, predictions inform critical mitigation decisions, necessitating high-fidelity predictions across a range of behaviors that dynamic systems are likely to exhibit. We identify various sources of uncertainty in the modeling pipeline and propose mitigative measures to reduce or manage these uncertainties. In hardware-based malware detection, we first perform online uncertainty estimation to monitor predictions post-deployment, recognizing the model's limitations in classifying unknown behavior as benign or malicious. Next, we develop data and inductive biases to accurately capture malware behavior, reducing uncertainty that manifests as an overlap between the manifolds representing the benign and malware classes. Finally, we address irreducible uncertainty in the context of stochastic wildfire modeling by proposing metrics that test the model's ability to capture stable and critical behaviors of the system, even in the presence of inherent randomness.