There’s no place like Tiffany, the famous jeweler says on its website — and that includes Costco.

A federal district court judge has ordered Costco to pay Tiffany more than $19 million for selling generic diamond engagement rings that were marketed using Tiffany’s name.

The rings in question had a pronged setting that Costco said is “commonly known as a ‘Tiffany’ setting.” Some of the display cases, however, simply described the rings as “Tiffany” instead of “Tiffany setting” or “Tiffany style.”

Judge Laura Taylor Swain ruled Aug. 14 that Tiffany is entitled to $11.1 million as profits for trademark infringement, plus interest, and $8.25 million in punitive damages, which was awarded by a jury in October.

Swain also said that Costco was permanently prohibited from using “Tiffany” as a stand-alone term when selling its products.

Tiffany’s lawsuit, filed in 2013 on Valentine’s Day, was the equivalent of sending Costco a black rose.

Tiffany sued after it discovered that salespeople at Costco were responding to customer inquiries by calling certain solitaire diamond rings “Tiffany” rings.

Furthermore, the salespeople “were not perturbed when customers who then realized that the rings were not actually manufactured by Tiffany expressed anger or upset,” Swain wrote.

“Tiffany has never sold nor would it ever sell its fine jewelry through an off-price warehouse retailer like Costco,” the lawsuit said.

Costco said in a statement that it plans to appeal the ruling, which it described as “a product of multiple errors in pretrial, trial, and post-trial rulings.”

“This was not a case about counterfeiting in the common understanding of that word — Costco was not selling imitation Tiffany & Co. rings,” Costco said, emphasizing that the rings were not marked with the Tiffany name and were not sold using Tiffany’s trademark blue boxes.

The judge was not swayed by these arguments, however.

“Costco’s upper management, in their testimony at trial and in their actions in the years prior to the trial, displayed at best a cavalier attitude toward Costco’s use of the Tiffany name,” Swain wrote.

With the exception of Tiffany’s limited collaboration with Net-a-Porter, Tiffany jewelry is available only at Tiffany stores, a Tiffany spokesman said in an email.

“Judge Swain’s decision validates the strength of the Tiffany trademark and the value of our brand, and most importantly, sends a clear and powerful message to Costco and others who infringe the Tiffany mark,” the company said in a statement.