The phrase "were above board" implies honesty, transparency, and fair play. Therefore, some antonyms for this phrase could be "underhanded", "devious", "dishonest", "unscrupulous", or "sneaky". These words suggest a lack of integrity and a tendency to act in an unethical or dubious manner, especially in business dealings. Being "above board" is desirable because it indicates a willingness to play by the rules and maintain high standards of conduct. On the other hand, those who are "not above board" may resort to trickery, deceit, or shady practices to gain an advantage or deceive others.