Heavyweight deep geometric descriptors have achieved impressive accuracy in point cloud registration but remain impractical for real-world deployment due to their high storage demands and slow inference. To relieve it, we propose 3DMatch-KD, a knowledge distillation framework tailored for 3D matching, facilitating the training of a lightweight student geometric descriptor under the guidance of a heavyweight teacher one. Specifically, our 3DMatch-KD comprises a contrastive loss-based local matching distillation and an optimal transport-guided global matching distillation. The local distillation leverages contrastive loss to enforce consistent point-to-point local geometric representations between student and teacher descriptors, enforcing their pointwise feature consistency. Meanwhile, the global distillation aligns the student’s geometric feature distribution with the teacher’s via optimal transport, enhancing their overall feature consistency. Extensive experiments demonstrate that 3DMatch-KD significantly reduces the model size of state-of-the-art deep descriptors while maintaining high registration accuracy, validating the effectiveness of our proposed method.