In the Valpolicella area (Verona, Italy) one of the most important Italian wines is being produced: Amarone, predominately made by Vitis vinifera cv. Corvina. This wine is subjected to a specific postharvest process, namely, withering, which aims to increase alcohol content and/or high residual sugars while retaining richness in aromas and organoleptic compounds. In accordance with guidelines and strict Amarone protocol set by the Consorzio of Amarone-Valpolicella, withering must be carried out by setting the grapes in a suitable environment. In our study, the withering process was performed following the traditional methods, i.e., in open-air, natural environmental conditions, as generally performed by winegrowers, leading to a weight loss in grapes of up to 30%. Whilst the effect of different postharvest conditions is clear and studied, it is interesting to know how soil can affect both grapes and wine profile, in terms of aromas, which are of great importance for this crafted wine. For this purpose, for two study years, the influence of two different sites (with regards to the carbonates’ content) on aromas were investigated. Furthermore, microvinifications and the sensory profile of the resulting wines were analysed. Our results clearly indicated that different soils’ characteristics, particularly differences in carbonate content, had an important effect, not only on the aromatic compounds of grapes and wines, but on the sensory profile as well. This information will help winegrowers and winemakers in the process of determining site selection for future vineyards in order to obtain a final optimum Amarone wine, in terms of its aromatic composition—one that is able to respond to the market demand.