The aromatic profile of a wine is one of the main characteristics appreciated by consumers. Due to climate change, vineyards need to adapt to new conditions, and one of the strategies that might be followed is to develop new white varieties from Monastrell and other cultivars by means of intervarietal crosses, since white varieties are a minority in south-eastern Spain. Such crosses have already been obtained and have been seen to provide quality white wines of high acidity and with a good aromatic composition. To confirm this, a quantitative analysis was carried out during two vintages (2018 and 2019) in order to study and compare the volatile composition of Verdejo (V) wine with the aromatic composition of several wines made from different crosses between Cabernet Sauvignon (C), Syrah (S), Tempranillo (T), and Verdejo (V) with Monastrell (M), by means of headspace SPME-GC-MS analysis. Wine volatile compounds (alcohols, volatile acids, ethyl esters, terpenes, norisoprenoids, and two other compounds belonging to a miscellaneous group) were identified and quantified using a HS-SPME-GS-MS methodology. An additional sensory analysis was carried out by a qualified tasting panel in order to characterize the different wines. The results highlighted how the crosses MT103, MC69, and MC180 showed significant differences from and better quality than the Verdejo wine. These crosses produced higher concentrations of several aromatic families analyzed, which was supported by the views of the tasting panel, thus confirming their excellent aromatic potential as cultivars for producing grapes well adapted to this area for making white wines.