The possibility of not being alone in the Universe and of finding another form of civilization has always been an interesting and controversial topic. In this paper we are developing a model for the detection of intelligent life-markers on Earth-like planets transiting white dwarfs, by analyzing their atmospheres. It has already been noted that white dwarfs have long-lived habitable zones that may be hosting planets (3 Gyr), which is why we are pointing towards them as a potential source for the future discovery of other intelligent civilizations. The way we are testing whether or not these planets are strong candidates for hosting intelligent life is by analyzing their atmospheric transmission. By performing simulations of the James Webb Space Telescope (JWST) spectroscopic observation of an Earth- like planet transiting a white dwarf star, and further focusing our results in the Near-Infrared part of the spectrum, we can check for the molecules present in the atmosphere of the planet. We are particularly looking for given molecules that we know to be produced by artificial means (such as industrial pollution) in the Earths atmosphere. We are reasoning our results on the basis that if we are able to detect these molecules in the atmosphere of Earth-like planets orbiting white dwarfs, then there must be some form of civilization on these planets, which is producing the elements we are looking for.