I was lucky that an ancestor married in October of 1870 a few months after the census. Finding her parents was a little more difficult. I searched for everyone with her name in the 1870 census, searching the census in a circle with a 15 or so mile radius of where she married in 1870. Then I researched every person with her name in 1870 and eliminated those that couldn't be her.
The key was that I didn't just grab the "first one" I found and that I also used variant spellings even after I had a match on the "right name," just in case.