Underwater images, often affected by light attenuation and particle scattering, pose a challenge for restoration, aggravated by the difficulty in obtaining a substantial amount of annotated data. Existing methods have tackled this issue through the development of semi-supervised frameworks; however, they commonly lack a suitable strategy or rely on additional models trained on extra data to ensure the quality of pseudo-labels. To address this, we propose a self-assessment training framework for semi-supervised underwater image restoration (SAT-UIR). SAT-UIR employs a dual-task network (DT-Net) incorporating an auxiliary assessment task to align the restored image with a target structure similarity index measure score. This enables accurate restoration completeness estimation at a feature level and effective pseudo-label filtering during self-training. Leveraging multi-scale features, the assessment task also encourages the model to learn advantageous features for image restoration. Moreover, we integrate a soft ranking loss to further refine the training process of the auxiliary assessment task. Comprehensive experiments on various underwater benchmarks demonstrate that SAT-UIR outperforms state-of-the-art methods quantitatively and qualitatively. The code is available at https://github.com/aroid721/SAT-UIR.