Printing is a widespread industrial process. Manufacturers of colored products are expected to maintain high levels of color quality to perfectly satisfy the customers' requirements. The rendering of colors is visually checked by experienced workers, who may though show different color sensitiveness, depending, e.g., on perceptual, cognitive and cultural aspects. This often results in products that fail to faithfully reproduce what the customer asked for, with negative consequences for companies, as well as huge financial losses. This paper describes a neural network-based system to objectively check how faithfully colors are reproduced by an industrial printing process. The system considers a master color, then compares it to a copy, and returns an objective degree of color fidelity of the copy to the master. The neural system was trained and tested in a real-world case study by using a huge quantity of color pairs taken from the L*a*b* color space. Highly accurate results were achieved. The strengths of the system are that it can measure the difference of colors in a way that is incredibly close to that perceived by the human eye, and the fact that it can do that canceling the color distortion phenomena that may occur in the human vision.