The word "unsoundest" refers to something that is not secure or reliable. The antonyms for "unsoundest" would be words that describe something that is solid, stable, and dependable. These antonyms might include terms like secure, trustworthy, strong, stable, reliable, robust, and sound. When we speak of a sound argument, we mean one that is based on reliable evidence and reasoning. To have sound judgement is to make wise, informed decisions that are based on a solid foundation of information. By contrast, unsound arguments and unsound judgement are based on flawed reasoning or inaccurate information. So, the antonyms for "unsoundest" are words that suggest something that is trustworthy, well-built, and dependable.