How can I explicitly teach metacognitive problem-solving strategies in HS math?

[Matthew32]

I'm a high school math teacher, and I'm redesigning my curriculum to place a stronger emphasis on developing my students' mathematical problem solving strategies rather than just rote procedure. I want them to learn how to approach unfamiliar, non-routine problems with confidence, but I'm struggling to teach the metacognitive skills of analyzing a problem, selecting a strategy, and checking their work. For other educators, what are the most effective ways you've found to explicitly teach and model these strategies in the classroom? How do you create a learning environment where students feel comfortable taking risks and sharing their thought processes, even when they lead to a wrong answer, and what types of problems best foster this kind of strategic thinking?