Sentimental emotions in a story are always unearned emotions. They are manipulative, they cheat the reader and expose the author as a fraud.
I suppose Tolstoy could be accused of sentimentality but that would be wrong. Tolstoy earns every emotion and everything that happens is because of the characters. If a character is sentimental, so shall the story go. If there is a coincidence, so too shall the story go.