The use of pomace in bakery products opens up new possibilities for the management of waste products from the fruit industry. Such activities are integral to the concept of sustainable development and the circular economy. In this research, the quality of dough and final products was analyzed by replacing 10–50% of the typical flour (wheat, rice, and corn) with chokeberry pomace flour. The instrumental color measurements and the sensory analysis showed that the dough and the muffins made with the fruit flour were significantly different from the control samples. Flour substitutions of over 10%, while enriching muffins with chokeberry flour, led to a decrease in product quality (texture, dough rise, sensory quality), especially for muffins with gluten. The sensory study showed that a substitution of 10% of typical flour resulted in products acceptable to potential consumers, but a higher substitution reduced the overall quality. It was found that the use of chokeberry pomace in making muffins was limited and more feasible for gluten-free products.