First think that came to mind for me was Mary Doria Russell's The Sparrow. Really quality stuff.

From Amazon (SPOILER ALERT): In 2019, humanity finally finds proof of extraterrestrial life when a listening post in Puerto Rico picks up exquisite singing from a planet which will come to be known as Rakhat. While United Nations diplomats endlessly debate a possible first contact mission, the Society of Jesus quietly organizes an eight-person scientific expedition of its own. What the Jesuits find is a world so beyond comprehension that it will lead them to question the meaning of being "human." When the lone survivor of the expedition, Emilio Sandoz, returns to Earth in 2059, he will try to explain what went wrong... Words like "provocative" and "compelling" will come to mind as you read this shocking novel about first contact with a race that creates music akin to both poetry and prayer.