The scarcity of paired data severely limits the performance and generalization of learning-based underwater image enhancement (UIE) methods. This challenge is particularly prominent in scenes with complex degradations. Semi-supervised learning has emerged as a promising solution by enabling the utilization of large-scale unlabeled data. However, its effectiveness is limited by the use of static, model-agnostic metrics for pseudo-label reliability assessment. To address this, we propose SEA-PACE, a novel semi-supervised framework that integrates model-aware uncertainty modeling and self-paced consistency learning to fully exploit unlabeled data for UIE. Specifically, we design a Model-Aware Reliability Estimator (MARE) that quantifies the uncertainty of the teacher model's predictions through Gaussian Process Regression in latent feature space. The resulting uncertainty is then transformed into reliability weights via a rank-based mapping. Additionally, we apply the Self-Paced Consistency Learning (SPCL) strategy that employs a loss-aware schedule to dynamically prioritize high-confidence pseudo-labels, gradually incorporating more challenging samples during training. Extensive experiments on several public UIE benchmarks demonstrate that SEA-PACE consistently surpasses state-of-the-art methods in both visual quality and generalization capability. The code is publicly available at: \url{https://github.com/haigouboss/SEA-PACE}