Are either of those commas after said ever necessary?
Hello, ForestDreams, and welcome to the Grammar Exchange.
The following sentences are not incorrect:
(1b) "What a night," Shelia said before disappearing into the crowd.
(2b) "That was delicious," Shelia said with a smile.
However, I prefer the original versions, with those commas restored:
(1a) "What a night," Shelia said, before disappearing into the crowd.
(2a) "That was delicious," Shelia said, with a smile.
I think the "before"- and "with"-phrases are most naturally understood as providing a supplementary detail, and that makes the comma desirable, just as we use commas before nonrestrictive appositives (e.g. "John's wife, Mary").
If, however, the "before"- and "with"-phrases are intended by the writer to provide information central to the whole point of the sentence, they need not be set off with a comma.
If they provide essential details, they are essentially answering the questions "What did she say before disappearing into the crowd?" and "What did Sheila say with a smile?" Such questions would only need answering in special contexts.
Consider, too, as a point in favor of the commas, that were the sentences to be rearranged such that the "before"- or "with"-phrases came first, or such that there was inversion in the clause of attribution, the commas would be desirable:
(1c) Before disappearing into the crowd, Sheila said, "What a night."
(2c) With a smile, Shelia said, "That was delicious."
(1d) "What a night," said Sheila, before disappearing into the crowd.
(2d) "That was delicious," said Sheila, with a smile.