1 A stainless steel chimney cap cost $50 to $500. 2  Copper chimney caps cost $200 to $2,000 or more. 3  Decorate chimney caps and custom chimney caps cost $500 and up. 4  Chimney cap installation costs an additional $100 to $200 and up.omplete the form at the bottom of the page for the most accurate chimney cap costs. 1  A galvanized metal chimney cap costs $50 to $200. 2  A stainless steel chimney cap cost $50 to $500. 3  Copper chimney caps cost $200 to $2,000 or more.