Face Super-Resolution (FSR) is a specialized task within the broader field of super-resolution (SR) research, aimed at enhancing low-resolution facial images for applications in security, facial recognition, and digital imaging. Unlike general SR, FSR presents unique challenges, as artifacts can significantly compromise facial analysis, with even minor distortions leading to substantial errors. While recent advancements in SR have improved image quality, their applicability to real-world degraded images remains under researched. This study proposes a novel FSR training methodology that combines knowledge distillation (KD) and a frequency-domain loss function to address real-life degradation and assess the impact of super-resolution on face identification (ID) accuracy. Furthermore, a fine-tuning process is introduced to enhance the performance of face ID models on super-resolution images. Experimental results indicate notable improvements in reconstruction quality and face ID accuracy across various models, particularly lightweight models. This work underscores the potential of integrating KD and frequency-domain techniques to advance SR researchs and expand their applications beyond FSR.