Miller has been part of the club since 2010, while Braid joined the team at the start of the year.
"I have enjoyed my three seasons at the club and was delighted to agree a new deal. We have some great young players who have come through the system and we also have some great experienced players too," Miller told the club's website.
Braid added: "I came over here the first week of 2013 when [director of rugby Steve Diamond] signed me and everyone at the club has made me and my family very welcome.
"We have some good players here at Sale Sharks and I am looking forward to spending my time here in the North-West."
The Sharks are currently bottom of the league table.