Do not break sentences in two.
In other words, do not use periods for commas.
I met them on a Cunard liner many years ago. Coming home from Liverpool to New York.
She was an interesting talker. A woman who had traveled all over the world and lived in half a dozen countries.
In both these examples, the first period should be replaced by a comma and the following word begun with a small letter.
It is permissible to make an emphatic word or expression serve the purpose of a sentence and to punctuate it accordingly:
Again and again he called out. No reply.
The writer must, however, be certain that the emphasis is warranted, lest a clipped sentence seem merely a blunder in syntax or in punctuation. Generally speaking, the place for broken sentences is in dialogue, when a character happens to speak in a clipped or fragmentary way.