"Aymer" is a variation of Aylmer (click on blue link for meaning).
"Ewing" is a surname of Scottish origin, a variation of "Ewan", which itself is an Anglicized form of the Gaelic personal name Eoghan.
I can't find my book of tartans right now, so I don't know if there is a tartan connected to the name. Daividh, who posts here, may have some tartan books and be able to help you. Otherwise, I'll keep looking around my house for the book. But even if I find the book, it won't be much help to you because all I can do is describe what the tartan looks like. Better you should head to your local public library and see if they have a book with illustrations of the various tartans.