This work aimed at giving a comprehensive and in-detailed guide on the route to fine-tuning Convolutional Neural Networks (CNNs) for glaucoma screening. Transfer learning consists in a promising alternative to train CNNs from stratch, to avoid the huge data and resources requirements. After a thorough study of five state-of-the-art CNNs architectures, a complete and well-explained strategy for fine-tuning these networks is proposed, using hyperparameter grid-searching and two-phase training approach. Excellent performance is reached on model evaluation, with a 0.9772 AUROC validation rate, giving arise to reliable glaucoma diagosis-help systems. Also, a benchmark analysis is conducted across all fine-tuned models, studying them according to performance indices such as model complexity and size, AUROC density and inference time. This in-depth analysis allows a rigorous comparison between model characteristics, and is useful for giving practioners important trademarks for prospective applications and deployments.