"Keep a stiff upper lip" is a popular idiom that means to remain brave and resolute in the face of adversity or emotional distress. If you're looking for synonyms that carry a similar meaning, you might consider the expressions "keep your chin up," "stay strong," "stand firm," "endure," or "persevere." Other phrases like "put on a brave face," "maintain composure," or "keep it together" can also be used to convey a similar sentiment. Ultimately, the key idea behind these expressions is to encourage someone to remain steadfast and remain hopeful in difficult situations.