We all know that there must be a comma in front of a coordinate conjunction that has a complete sentence after it.
...went with her, and she declined the assistance.
...was standing nearby, but there was no opportunity to speak up.
Sometimes there is an element right after that conjunction that needs commas around it.
...went with her, and, well, she declined the assistance.
...was standing nearby, but, Mr. Barker, there was no opportunity to speak up.
Because there is a need for the comma that separates the two sentences to really stand out and because it is somewhat obscured by the commas immediately after it, the comma before the conjunction -- by far, the most important comma in the sentence -- needs to be "upgraded" to a semicolon.
...went with her; and, well, she declined the assistance.
...was standing nearby; but, Mr. Barker, there was no opportunity to speak up.
Happy punctuating!
Margie