This is what we found out: Glenmorangie Cellar 13 was originally launched in 1998. If you require a precise date for this particular bottle, then please look for the Lot Code - that is, the code normally found printed on the outside of the base of the bottle. (usually in the form or similar to "L4 350 10.22 4ML"). With this information, we should be able to have your bottle dated.
Some background information on Glenmorangie Cellar 13:
Cellar 13 was matured for 10 years in "American Mountain Oak" in the Glenmorangie Distillery's Cellar 13, a low, stone-walled and slate-roofed warehouse on the shores of the Dornoch Firth built and slate. The tasting notes mention that only 1st fill casks were used for the original Cellar 13 bottlings.
Hope this helps!