Quince (Cydonia oblonga Miller) is a plant that is commonly cultivated around the world, known for centuries for its valuable nutritional and healing properties. Although quince fruit are extremely aromatic, due to their high hardness and sour, astringent, and bitter taste, they are not suitable for direct consumption in an unprocessed form. However, they are an important raw material in fruit processing, e.g., in the production of jams, jellies, and juices. Quince fruits fall under the category of temperate fruits, so their shelf life can be predicted. Considering that technological processing affects not only the organoleptic properties and shelf life but also the functional properties of fruits, the aim of this research was to determine the impact of various types of technological treatments on the physicochemical and bioactive properties of quince fruit. In fresh, boiled, and fried fruits and in freshly squeezed quince fruit juice, basic parameters, such as the content of dry matter, moisture, soluble solids (°Brix), pH, total acidity, water activity, and color parameters (L*a*b*) were determined. The content of key bioactive ingredients, i.e., tannins, carotenoids, flavonoids, phenolic acids, and total polyphenols, was also determined, as well as the antioxidant activity of raw and technologically processed (cooked, fried, and squeezed) quince fruits. The conducted research showed that fresh quince fruit and processed quince products can be a very good source of bioactive ingredients in the diet, such as tannins (3.64 ± 0.06 mg/100 g in fresh fruit; from 2.22 ± 0.02 mg/100 g to 5.59 ± 0.15 g/100 g in products), carotenoids (44.98 ± 0.18 mg/100 g in fresh fruit; from 141.88 ± 0.62 mg/100 g to 166.12 ± 0.62 mg/100 g in products), and polyphenolic compounds (246.98 ± 6.76 mg GAE/100 g in fresh fruit; from 364.53 ± 3.76 mg/100 g to 674.21 ± 4.49 mg/100 g in products). Quince fruit and quince products are also characterized by high antioxidant properties (452.41 ± 6.50 µM TEAC/100 g in fresh fruit; 520.78 ± 8.56 µM TEAC/100 g to 916.16 ± 6.55 µM TEAC/100 g in products). The choice of appropriate technological processing for the quince fruit may allow producers to obtain high-quality fruit preserves and act a starting point for the development of functional products with the addition of quince fruit in its various forms, with high health-promoting values and a wide range of applications in both the food and pharmaceutical industries.