The CLIP model has been recently proven to be very effective for a variety of cross-modal tasks, including the evaluation of captions generated from vision-and-language architectures. In this paper, we propose a new recipe for a contrastive-based evaluation metric for image captioning, namely Positive-Augmented Contrastive learning Score (PAC-S), that in a novel way unifies the learning of a contrastive visual-semantic space with the addition of generated images and text on curated data. Experiments spanning several datasets demonstrate that our new metric achieves the highest correlation with human judgments on both images and videos, outperforming existing reference-based metrics like CIDEr and SPICE and reference-free metrics like CLIP-Score. Finally, we test the system-level correlation of the proposed metric when considering popular image captioning approaches, and assess the impact of employing different cross-modal features. Our source code and trained models are publicly available at: https://github.com/aimagelab/pacscore.