NOTE: Based on the link I have listed here, Borders is also a German surname.
http://www.familytreedna.com/group-join.aspx?Group=Borders
This group of people need for you to get a one of the following Y-DNA tests done:
Requirements
A Surname Project traces members of a family that share a common surname. Since surnames are passed down from father to son like the Y-chromosome, this test is for males taking a Y-DNA test. Females do not carry their father's Y-DNA and acquire a new surname by way of marriage, so the tested individual must be a male that wants to check his direct paternal line (father's father's father's...) with a Y-DNA12, Y-DNA37, or Y-DNA67 marker test. Females who would like to check their direct paternal line can have a male relative with this surname order a Y-DNA test. Females can also order an mtDNA test for themselves such as the mtDNA or the mtDNAPlus test and participate in an mtDNA project
http://www.familytreedna.com/test-descriptions.aspx
You are going to have to go to great lengths and research out your surname to see if it has any lineage that would give you the right to a coat of arms.
You may find that after all your research, your surname (based on lineage) doesn't have a coat of arms
I have left this link just in case you wanted to consider it.
http://www.4crests.com/borders-coat-of-arms.html
From this same link, I put my step-son's last name in (Tomesch)--http://www.houseofnames.com/fc.asp?sId=&s=Tomesch
They show the search to come up empty. Draw your own conslusions as to whether they are legitimate or not.
I will state that I do agree with everyone that the above site is more than likely not worth your while. I left it for your sake to make your own decisions about it.
Search FAQs
Where do I find my family’s coat-of-arms?
No family or surname “owns” a coat-of-arms. Arms are owned by an individual who has had them registered with a government official, such as the Lord Lyon, King of Arms in Scotland. Using a coat-of arms that does not belong to you is illegal and disrespects the customs and traditions of heraldry.
From the Introduction to "In Search of your British and Irish Roots" by Angus Baxter.
“Do not be led astray by advertisements offering you a coat-of-arms and a family history…unlikely you or your family have any right to a coat-of-arms…All you will get for your money is a coat-of-arms originally granted a long time ago to someone with a similar surname to yours. The odds against that person being your ancestor are great, and in any case, a coat-of-arms only descends from eldest son to eldest son.” p. xii
For more information about heraldry, please visit the following web sites:
http://www.heraldry-scotland.co.uk/ -- contains many articles about heraldry, coats-of-arms, and many links to other organizations.
http://www.college-of-arms.gov.uk/
http://www.theheraldrysociety.com/index.htm
http://heraldry.ca/
http://www.americancollegeofheraldry.org/
http://www.heraldica.org/ has many Frequently Asked Questions about Heraldry.
A search of the catalog with the subject Heraldry will turn up numerous resources--http://thelibrary.springfield.missouri.org/faq/files/lhcofh.cfm
Where to find arms on the Web?
The next most-popular question is:
Is there a Web site of FTP site where I can look for my arms?
The answer is: No (in general: see below). No one has compiled all or even the main armories into a scholarly database; and if anyone had, it is understandable that they would be reluctant to provide the fruits of so much effort for free. If you want to look for arms born by families with the same name as yours, you need to go to a library and consult armories.
On the French Minitel (36 17),http://www.absoluteastronomy.com/topics/Minitel
there is an armory look-up which will return the coat of arms when supplied with a last name, and also provide references. This service is not accessible through the Web, it is in French, and it is not free. There are other services on the Web which will look up a name and return a coat of arms for a fee, though they usually do not provide references. Look for them with the usual search engines--http://www.heraldica.org/questions.htm#where
I have posted these two other links that give meaning to your name. Hopefully they can help you out some.
This first link, they are looking for others with that surname to join with them in searching out their origins. They have compiled a very interesting background of that surname.
http://www.familytreedna.com/group-join.aspx?Group=Borders
http://www.ancestry.com/facts/Borders-family-history.ashx