When we use the phrase "broke out in a sweat," we generally mean that we started sweating excessively or suddenly due to fear or stress. The antonyms for this phrase could be "stayed calm and composed," "remained cool and collected," or "didn't break a sweat." These phrases imply that the person did not experience any overwhelming fear or anxiety that would lead to excessive sweating. Other antonyms for "broke out in a sweat" could be "relaxed and at ease," "peace of mind," or "unperturbed." These phrases indicate that the person is in a state of physical and emotional calmness and is not experiencing a fight-or-flight response.