Redmayne, who won the Best Actor Academy Award for his role as Stephen Hawking in 'The Theory of Everything', had paid tribute to both Woodburne and her on-screen husband Alan Fletcher, reported Digital Spy.
Responding to the tribute, Woodburne thanked Redmayne in a special video message where she also praised him for his own talent.
She said: "Congratulations Eddie on all the accolades on your beautiful performance, and thank you so much for the mention.
"It means more than I can tell you to all of us at 'Neighbours', not just myself and Alan. Thank you and good luck with everything you do in the future. Congratulations again."