There is so much beautiful music in the classical and romantic eras and it is shown vividly in the second movement [which is usually the slow romantic movement] of the great piano concerti. Here are some of the best.
Mozart piano concerto#21 http://tinyurl.com/6xhl77 "Elvira Madigan"
Mozart piano concerto#23 http://tinyurl.com/d6so8u
Mendelssohn piano concerto #2 http://tinyurl.com/26wua5o
here is a great violin concerto by Brahms [2nd movement] which is beautiful
Brahm's violin concerto http://tinyurl.com/ckumcs
and in my opinion the two most beautiful movements are in the following 2 posts