MENSTRIE, Scotland—In the last 200 years, there have been fewer Johnnie Walker master blenders than British monarchs. With only 14 years on the job, Jim Beveridge has barely passed his probation.

But for Diageo PLC, maker of the popular Scotch-whisky brand, Mr. Beveridge is indispensable. He could have the most valuable nose in the liquor business.

He uses his sensory talents to create individual blends of Scotch for clients who want much more than an expensive bottle from duty-free. The starting price for a case of your own signature blend? Around $130,000.

“I often get asked if my nose is insured,” Mr. Beveridge said. “It’s not, but I couldn’t do without it.”

Mr. Beveridge, the sixth master blender since John Walker distilled his first Scotch whisky in Kilmarnock, Scotland, in 1820, works in a booming industry.

Scotch exports hit an all-time high of £4.3 billion ($7.2 billion) in 2013, according to figures released in April by the Scotch Whisky Association, making up nearly a quarter of all British food-and-drink exports. Americans were the thirstiest for Scotch, buying nearly 20% of all exports in value terms.

The bespoke blending service Mr. Beveridge oversees—offered by Diageo at invitation-only Johnnie Walker emporiums in Shanghai, Beijing and Seoul—aims to tap into this demand. The company says it has produced only 10 signature blends since 2011. A bottle costs at least $6,500—often much more—with a minimum order of 20 bottles.

The demands from clients can be extreme. One customer plans to build a library full of whisky and ordered each bottle to be individually packaged to look like a book. Some clients have simpler requests, such as a smoky flavor or label designed around a family crest.