If the family name is of British, Scottish, Welsh, or Irish ancestry, the College of Heralds is the place to seek help.
Heralds have, down thru the centuries, been the people who design and authenticate, family coats of arms, and crests. They are the official arbiters of what, who, why, and when, as it applies to family heritage.
Do a GOOGLE search and see what the College of Heralds can do to help you.
Follow up question on previous response. What about a European (Polish,German,Swiss,etc.etc.)surname. Use the same resources??
Be very cautious in researching a family crest - the majority of people at that time did not have such an emblem, and were farmers, peasants, etc. There area lot of scam companies offering crests, lineages etc for a price.
Don't forget, just because you find an authentic crest for your Surname does not necessarily make your family eligible. You must find and authenticate a direct lineage to the proper family members to use a crest.