Localization in Global Navigation Satellite System-denied environments is critical for autonomous systems, where traditional simultaneous localization and mapping methods often lack generalizability. This paper presents an uncertainty-aware magnetic navigation framework that directly approximates information from the localization distribution to optimize trajectory selection. By minimizing information loss while ensuring goal attainment, it achieves improved accuracy and efficiency. Real-time simulation in a Global Navigation Satellite System-denied indoor environment, along with hardware validation, shows a localization performance of 5% higher, 34% lower failure rates, and more than 99% computational savings compared to state-of-the-art methods, with consistent results across different anomaly maps. These findings highlight the practicality and robustness of the solution for long-duration magnetic-based navigation. Code and usage can be found on the project website: https://theaprilab. github.io/info_magnav