In Brickwood Contractors, Inc. v. Datanet Engineering, Inc., the Fourth Circuit in an opinion by Judge Widener joined by Judges Wilkinson and Michael reversed an award of $15,000 in sanctions under Rule 11 because the moving party waited under the end of the case and failed to comply with the 21-day advance notice provisions required by Rule 11.
I guess what the defendant should have done in the case was to send out the Rule 11 notice at the same time as its motion for summary judgment. (And why not? It doesn't get filed.)
I think the only time that I sent out a Rule 11 notice was in a case with a pro se plaintiff, where Judge Turk had more or less told the plaintiff that if she did not drop the case, and then lost at trial, the defendant (whom I represented) would be asking for sanctions. So, I served the papers on the plaintiff, to set up a later motion under Rule 11, explaining what a bunch of nonsense the case was and how much money we would want from the plaintiff. In reply, she wrote to the Court, saying if these papers were meant to intimidate her, it worked, and she was dropping the case - an outcome I would never have expected.