The primary exception to the "no buyback" rule is the , specifically for engagement rings:

Personalized or custom-engraved items are typically ineligible for return or exchange. The Tiffany Diamond Upgrade Program

This is a trade-in program for store credit, not a cash buyback. Alternative Resale Options

For those who have recently purchased a piece and are experiencing "buyer's remorse," Tiffany & Co. offers a standard return window: