The segment starts off with Kate McKinnon as Clinton's wife Hillary, who is attempting to use her cellphone to tape her announcement that she plans to run for commander-in-chief in 2016.
"I am running because I want to be a voice for women everywhere," McKinnon as Hillary says before being interrupted by Hammond's Bill, who sticks his face in the video and asks, "Did someone say women everywhere?"
Hillary rolls her eyes and laughs, "Oh, Bill!"
"Hillary would make a great president and I would make an even greater first dude," Bill declares. "Hillary, isn't it crazy that phones can take videos now? If they could have done that in the '90s, I'd be in jail."
"Great, Bill. I love jokes about that," Hillary says, pushing his face out of the shot.
"OK, I get it. This election is about you. I don't want to hog your limelight. I am leaving. Look at me go," he says, backing away. "Bye, I'm gone."
"Aren't we such a fun, approachable dynasty?" Hillary says to the camera, after which Bill can be seen and heard in the background playing a saxophone.
Hammond, 59, was an SNL cast member from 1995 to 2009. He returned to the sketch comedy series last year to replace the show's late announcer Don Pardo.