I called up Martin Gardner in 2007 and interviewed him about his connection to Nabokov. He was kind and generous with his time. He had not been familiar with Nabokov until reading Pale Fire. He liked the book, and he quoted the book in The Ambidextrous Universe.
Nabokov later counter-quoted him in Ada (see below***). Gardiner expressed sincere disappointment that Nabokov "spelled my name wrong!" (I don't have time to go back and listen to the recording of the interview right now, but the quote was very close to this). My recollection was that the two were not in correspondence before or during Pale Fire and did not communicate directly even after it--just a mutual admiration and acknowledgement in their books.
As of last year, Gardner was in an assisted living facility in Oklahoma, but had written a book on Chesterton that was slated to come out in 2007. He's 94!
***Here is a GoogleBooks link to Gardner's written description of the exchange between the two, from p. 73 of The Philosophy of Right and Left:
All private editorial communications, without exception, are read by both co-editors.
All private editorial communications, without
read by both co-editors.