The phrase "am of significance" implies importance or relevance. It's antonym, "am of insignificance," suggests a lack of value or unimportance. Other antonyms could include "unremarkable," "unnoteworthy," or "unimpressive." Opposite words could also include terms such as "trivial," "unworthy," or "insubstantial." The word "am" is a form of the verb "to be," which expresses the state or quality of existence. Therefore, the antonyms of this phrase could convey a range of meanings, such as triviality, irrelevance, or even negativity.