Meghan and her new grandmother-in-law were all smiles as they took in the sights.
Perhaps indicative of how she is learning the royal ropes, at one point the Duchess appeared confused over who should enter the royal auto first and resorted to asking the Queen what her preference would be.
During the event, Meghan and the Queen were also treated to a dance performance by local school children who were celebrating the 1,000 years of crossings over Mersey River.
Firstly, the Queen and Meghan will attend a lunch at Chester Town Hall, followed by official opening the Mersey Gateway Bridge.
Mexico's Rafa Marquez becomes third man to play at five World Cups
Kimmich lashed over from 25 yards and then Werner went to ground on the edge of the Mexico area, only for play to be waved on. It took Mexico 56 years to win a World Cup opener - their victory coming at the ninth attempt on home soil at Mexico 1986.
Outcry at flashing scenes in 'Incredibles 2' prompts epilepsy warning
In 2004, " The Incredibles " grossed $70 million in its opening weekend and ended up taking in a total of $633 million worldwide. The second frame of Warner Bros.' " Ocean's 8 " should land in second place with about $20 million from 4,145 domestic sites.
Sony's E3 Showcase Was Disjointed, But Was It What Gamers Wanted?
Great in concept, and with space for third party announcements between, it's hard to say that Sony managed to pull it off. It was impressive and the flawless demo for a game that is surely at the top of many people's wish lists.
"In the main floor at @Storyhouselive, The Queen and The Duchess of Sussex sit to view a performance of 'Drop in the Ocean.' #RoyalVisitCheshire", Kensington Palace tweeted.
Sharon Briscoe, a 61-year-old fan of Meghan and the royal family, was caught on film asking the Duchess how she was enjoying her new life as a married woman. "She is with the boss, so no pressure!"
And she certainly didn't disappoint, choosing a classic monochrome look that was understated and stylish.
While yesterday may have been a crash course from the Queen in public engagements, one element Meghan's certainly got right already is her occasion-wear wardrobe. She wasn't in the final season quite as much and that category is expected to be pretty competitive, with Thandie Newton from Westworld, Millie Bobby Brown from Stranger Things, and Alexis Bledel from The Handmaid's Tale all in the running.