Bernadette's due date arrives but she still hasn't given birth. As Amy and Howard work together at the college, the rest of the friends try various ways to initiate her labor, though Sheldon wants to play a complicated board game instead. Amy shocks Howard by saying Bernadette has already decided to name the baby after her father, Michael. He doesn't agree and everyone makes suggestions as to what to name the baby. Bernadette goes into labor and gives birth to a son named Neil, after Neil Armstrong, Neil Gaiman, and Neil Diamond, with Michael as the middle name. At the last minute, Howard relents to name him Michael as Bernadette got six stitches.
Amy and Howard begin collaborating on a neuroprosthetics project, upsetting Sheldon and Raj, who feel they are not spending as much time with them. When they seek solace with an annoyed Bernadette, she exploits the situation to trick Sheldon into doing Howard's chores. Penny successfully employs the approaches recommended in one of Bernadette's parenting books to deal with Sheldon, but Leonard believes she is coddling Sheldon too much. Sheldon and Raj resolve the issue of missing their significant others by spending time together.
Sheldon and Amy decide on a wedding date of May 12th. They want to have their reception at the Athenaeum at Caltech. While scouting the location, they are shocked to see Leonard and Penny eating there, as Leonard had told Sheldon their application had been denied. In reality, Leonard just wanted a place to avoid Sheldon. Kripke has booked the venue for his birthday party on the same day as the wedding. Leonard cleans radioactive sludge for Kripke to get the date for Sheldon as an apology for lying. Kripke eventually agrees to change the day but when Amy hears he wants to sing at the wedding, she suggests they get married at the Griffith Observatory instead. Meanwhile, Bernadette and Howard are unsure if one of them should quit their job to stay home with the children. Howard volunteers, but when left alone with the children he passes out exhausted, leaving Raj in charge. When Bernadette meets Penny for lunch, she realizes that she loves being at the office again, but doesn't want to leave the children. She and Howard promise to figure it out later after they take a nap.
According to Steve Holland who is the show-runner starting with this season, Wil Wheaton will return in this season since his absence from Season 10. And this has confirmed to be true since it has been stated that he reappeared in "The Proton Regeneration" (S11E6), along with Professor Proton, their first appearances since "The Opening Night Excitation" (S9E11) and "The Celebration Experimentation", respectively and a span of 43 episodes and a span of 37 episodes, respectively. Wil also returned in the 15th episode. Wil will also return for Sheldon and Amy's Wedding.
Leonard tells Zack and Marissa he will father their child, but Penny tries to seduce him despite knowing he has to be abstinent for a few days. Her visiting father, Wyatt, points out her actions suggest she is more conflicted over having kids than she lets on, which she admits. Wyatt says he will support her no matter what. Meanwhile, Sheldon and Amy warn that he will not be allowed to raise a child that is not his. Leonard decides not to go through with it; he tells Zack to have Sheldon be the donor, but Amy forbids it. Meanwhile, Howard turns Raj's cancelled bachelor party into a couples' trip into a zero-gravity aircraft, though he's convinced that Bernadette would hate it. Bernadette tries to get out of it so Howard sits out, forcing Bernadette to go through with it just to prove him wrong, though she does not enjoy it.
When Raj misses out on a job at the planetarium, his father says he has no confidence because Howard always makes fun of him. Raj distances himself from Howard and later gets the job. Howard is hurt by this (even after apologizing to him) and tries to make amends with Raj after his first performance at the planetarium but, when he sees him get a date, he leaves without speaking to him, thinking that the latter's life is better without him. Meanwhile, Sheldon and Amy try randomly dividing up wedding tasks, but they keep arguing. The only thing they can agree on is to get married, so they decide to just get married at City Hall. However, Sheldon decides that he wants a first dance with his new wife and they go home to plan their wedding.