If your family's name comes from the city of Glasgow, which is very possible, then you might never find a clan tartan. The clans were mostly in the highlands;, which had had a more feudal organization and governance. Many lowland family's were "affiliated" with or were considered septs of clans, but many were not. Consider the regional and universal tartans.

A quick search of the internet shows that some Glasgow families in the U.S. trace their roots back to Ulster, in northern Ireland, then to Scotland.