Automated landmark detection in lateral cephalograms has advanced significantly with deep learning. However, these methods typically rely on large-scale, well-annotated datasets, while medical image acquisition remains costly and accurate annotation demands substantial anatomical expertise along with intensive human effort. Semi-supervised learning offers a promising solution by leveraging unlabeled data to reduce dependence. This paper proposes a novel semi-supervised framework based on contrastive learning. Our method extracts landmark features and employs landmark-wise contrastive loss to cluster features of identical landmarks while repelling those of distinct ones. We capitalize on two inherent characteristics of cephalometric landmarks: (1) homologous anatomical points exhibit similar spatial patterns across patients, and (2) different landmarks demonstrate unique spatial signatures. Specifically, we integrate contrastive learning with a semi-supervised approach combining pseudo-labeling and the mean teacher method. This integration simultaneously reduces reliance on large-scale annotated data and enhances model robustness to anatomical landmarks across different imaging devices. Experiments on both public and in-house datasets demonstrate the effectiveness of the proposed method, which outperforms existing semi-supervised approaches.