According to William Shakespeare, Romeo and Juliet were married on
March 11th 1302. I can find plenty of references to this on the
internet, but nothing that explains where this nugget of information
comes from.

So the question: What is the evidence to suggest that William
Shakespeare had Romeo and Juliet getting married on March 11th 1302.

I do not believe Shakespeare gave a date. However, these citations
mention the marriage date of a real couple named Romeo and Juliet,
whose surnames are similar to "Montague" and "Capulet":

"Romeo Montocchio and Juliet Capelletto, the real couple upon which
Shakespeare based his play, 'Romeo and Juliet', were married at
Citadella, Italy March 11, 1302"

http://www.elreno.k12.ok.us/lincoln/parker.htm

"March 11... 
1302: Romeo Montevecchio and Juliet Cappelletto are married at
Cittadella in Italy."

http://webs.lanset.com/bookfolk/daybook_pages/march-2.htm