The phrase "two cents' worth" is often used to indicate one's opinion or viewpoint on a particular matter. However, there are several antonyms that can be used to convey the opposite meaning. Words like silence, neutrality, indecision, and ambivalence can be used to denote a lack of interest or indifference towards a topic. On the other hand, words like expertise, authority, knowledge, and experience can be used to indicate a highly valued and respected opinion. It is important to consider the context of the situation before deciding which antonym will be best suited to convey the intended meaning accurately.