Meghan is believed to get on well with The Queen after accompanying Her Majesty on a series of engagements in Cheshire in June, where they were pictured laughing and smiling together.
The Queen will be among members of the royal family attending a day of events to celebrate the RAF's centenary.
Meghan and Harry will have the opportunity to hear from female tech entrepreneurs at the lab. Meghan has always been a supporter of gender equality and programs that foster female empowerment and educational opportunities for women.
Queen Elizabeth and senior royals watched nearly 100 aircraft, from World War Two Spitfires to the newest stealth fighter jet fly over Buckingham Palace on Tuesday in a celebration to mark the 100th anniversary of Britain's Royal Air Force.
A trio of F-35B Lightning II aircraft of 617 Squadron taking part in the RAF100 flypast over London to mark the centenary of the RAF.More news: Trump admin hands over names of children under 5 separated at border
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The former Suits star has a penchant for bateau designs as she has donned the flattering open neckline on numerous occasions from various designers, including Dior for the Royal Air Force 100 service, Ralph Lauren at Prince Louis' christening, Prada during the Queen's Young Leaders Reception and of course Givenchy on her wedding day.
The centrepiece of RAF100 is today, with a service in Westminster Abbey, followed by a parade in The Mall and spectacular flypast over Buckingham Palace.
The royal couple will meet both President Michael D Higgins and Taoiseach Leo Varadkar during their relatively short two-day trip.
Markle kept her accessories in the same color family with a simple black clutch and wore her hair down - a contrast from the prim and proper chignon she wore earlier at the 100th anniversary celebration for Britain's Royal Air Force and upon touching down at Dublin Airport.
Although the royal couple's itinerary doesn't allow them the opportunity to visit famous attractions like Temple Bar and the Guinness Storehouse, they will still be introduced to Irish life at some other key sights that attract millions of tourists from around the world each year.