Some subjective choices of my own, in no real order-
*The Larghetto from Felix Draeseke's first sonata for viola alta and piano.
*The Andante (finale) from the first string quartet by Sergei Prokofiev.
*maybe that from Stenhammar's 4th string quartet (though more withdrawn, less on-its-sleeve. but still. The adagio- though the concluding Andante with variations movement could in some way qualify, it's the adagio 2nd movement I mean (though the andante finale is, really, even more charged...)... Or- the lovely B-flat minor Ostinato slow movement from his 3rd quartet... that's a very, very strong contender.)
(and there are some that I find myself humming quite alot, like that - in F-sharp major ...- of Robert Fuchs' 4th string quartet - already straying off-subject here.)
*not as Romantic (though very emotional)- the slow movements of the 2nd and 3rd of Arthur Honegger's string quartets.
Eric