Antonyms for the phrase "have significance for" can include "irrelevant," "unimportant," "insignificant," "meaningless," and "trivial." When something has no significance, it carries no weight or importance, and it may be disregarded or overlooked. Conversely, when something has significance, it has the power to affect or influence our thoughts and actions. Antonyms for this phrase can help us communicate the opposite of importance, such as when we wish to indicate that something holds no bearing on a particular matter. In contrast, the use of synonyms for "have significance for" can help emphasize the importance of a particular issue or event.