Sustainable irrigation strategies in Southeast Spain (one of the most arid regions in Europe) are essential to fight against desertification and climate change mitigation. In this way, Fondillon production is based on rain-based vineyards, over-ripe Monastrell grapes, and non-alcohol fortification. Thus, Fondillon is a naturally sweet red wine, protected within the Alicante Denomination of Origin, recognized by the European Union in its E-bachus database. The study aim was to evaluate the effect of the aging (solera factor) on Fondillon: (i) basic enological parameters (e.g., total, and volatile acidity), (ii) chromatic characteristics, (iii) antioxidant activity (ABTS(center dot+), FRAP and DPPH center dot), (iv) total contents of condensed tannins and anthocyanins, (v) volatile composition, (vi) sensory profile, and (vii) overall liking. Experimental data proved that the wine (1960 solera) with the highest total contents of condensed tannins and anthocyanins and total antioxidant activity was the most liked by Spanish consumers. Experimental results clearly established a positive relationship among Fondillon chemical composition, its antioxidant activity, and overall consumer liking. Exceptional harvest with grapes having extremely high antioxidant power (e.g., 1960 solera) will result, even more than 50 years later, in high quality wines with high consumer acceptance and a high monetary worth.