From Jacques Barzun’s From Dawn to Decadence: 500 years of Western Cultural Life, 1500 to the Present, pages 410-11:

But what is sentimentality? If one asks somebody who ought to know, one is told: an excess of emotion; or again, misplaced emotion. Both answers miss the point. Who can judge when emotion is too much? People vary not only in the power to feel and express feeling, but also in imagination, so that a stolid nature will deem it excessive as soon as love or grief is expressed vividly and strongly. Shakespeare is full of “exaggerated” emotion, but never sentimental. The same remark applies to the other answer. When is feeling misplaced? at the sufferings of the tragic hero? at the death of a pet? at the destruction of a masterpiece? One may argue that any emotion out of the common should be restrained in public, but that is another answer, one of social manners that has nothing to do with a feeling’s fitness to its occasion. The diagnostic test must be found somewhere else.

Sentimentality is feeling that shuts out action, real or potential. It is self-centered and a species of make-believe. William James gives the example of the woman who sheds tears at the heroine’s plight on the stage while her coachman is freezing outside the theater. So far is the sentimentalist from being one whose emotions exceed the legal limit that he may be charged with deficient energy in what he feels; it does not propel him. That is why he feels pleasure in grief and when he is in love never proposes. Sterne accurately entitles his story A Sentimental Journey: the tears he shed over the death of the donkey and his preoccupation with the girl at the inn caused him no upset nerves, no faster pulse or quickened breath. He reveled in irresponsible grief and love. This condition explains why the sentimentalist and the cynic are two sides of one nature. In such matters the arts are transparent and the connoisseur can easily tell imitation feeling from the real thing.