Endomicroscopy is an emerging imaging modality for real-time optical biopsy. One limitation of existing endomicroscopy based on coherent fibre bundles is that the image resolution is intrinsically limited by the number of fibres that can be practically integrated within the small imaging probe. To improve the image resolution, Super-Resolution (SR) techniques combined with image priors can enhance the clinical utility of endomicroscopy whereas existing SR algorithms suffer from the lack of explicit guidance from ground truth high-resolution (HR) images. In this article, we propose an unsupervised SR pipeline to allow stable offline and kernel-generic learning. Our method takes advantage of both internal statistics and external cross-modality priors. To improve the joint learning process, we present a Sharpness-aware Contrastive Generative Adversarial Network (SCGAN) with two dedicated modules, a sharpness-aware generator and a contrastive-learning discriminator. In the generator, an auxiliary task of sharpness discrimination is formulated to facilitate internal learning by considering the rankings of training instances in various sharpness levels. In the discriminator, we design a contrastive-learning module to mitigate the ill-posed nature of SR tasks via constraints from both positive and negative images. Experiments on multiple datasets demonstrate that SCGAN reduces the performance gap between previous unsupervised approaches and the upper bounds defined in supervised settings by more than 50%, delivering a new state-of-the-art performance score for endomicroscopy super-resolution. Further application on a realistic Voronoi-based pCLE downsampling kernel proves that SCGAN attains PSNR of 35.851 dB, improving 5.23 dB compared with the traditional Delaunay interpolation.