Sheaffer's dearly departed Burgundy is no doubt missed by more than just me. So, here are a couple of inks which are close, if not identical. The Burgundy has more of a red tone to it, the other two more of a gray. If anyone knows of a better match, please let me know. My lone remaining bottle of Burgundy can't last forever...

I may be mistaken by the scan and monitor, but Sheaffer's color is pretty darn close to Waterman's Violet. Have you tried it? It may be the perfect substitute for it.

Noodler's burgundy was close enough for me. I had a cartridge of Sheaffer's burgundy left to compare when I purchased the Noodler's. I didn't try the inks in the same pens, but I thought it was close.

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The new (made in Slovenia) Sheaffer Skrip Red (one of the close-to-center-spectrum red inks) is very safe for mixing, as is the new Skrip Purple (which is more blue-ish than reddish after it dries). I've mixed them with no chemical disasters and found interesting variations on the burgundy theme too.