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Hemmig shares the same origin as the Dutch surnames Hemminga and Hemmes and the Scandinavian surname Hemming. In fact, it partly has the same root as Hemingway.

The following link leads to a website with more information:
http://www.hemingway.uk.com/Derivations.htm

Best is to look at the surname Hemming, because Hemingway has also the component way . In short, Hemingr is an ancient Scandinavian firstname and Hemmig means you're ancestor beared that name. Hemingway means 'road to Hemming', i.e. 'road to the place where Hemming lives'.