Previous studies of prospective elementary mathematics teachers' mathematics anxiety have documented that many prospective teachers often worry about managing their repeated experiences of anxiety while developing their pedagogical and content knowledge to teach mathematics. The literature further indicates the importance of developing learning opportunities for prospective teachers to confront their past experiences while they (re)learn and learn to teach mathematics during methods courses. This study is situated within one such learning opportunity and seeks to analyze potential mathematics anxiety coping strategies generated by forty-eight prospective elementary teachers enrolled in a mathematical methods course. Written responses generated by the prospective teachers were subjected to qualitative thematic analysis to identify patterns of key ideas related to lesson planning for content they felt anxious and/or not confident about teaching and patterns focused on episodes of mathematics anxiety they might experience in the moment of teaching mathematics. Findings indicate that prospective teachers envision using between two and seven strategies grouped across eight coping strategy themes when given the opportunity to reflect on how they might deal with future instances of anxiety when they are tasked with teaching mathematics to their students. We highlight how some of the coping strategies that the prospective teachers envisioned as a means to cope with mathematics anxiety may have more potential to be helpful than others and present implications of our research for mathematics teacher educators.