It is reported that Markle and Queen's day is created to offer the 36-year-old a master-class on how to conduct royal engagements.
The pair are in Cheshire for their very first joint official engagement together.
Meghan will get plenty of quality time with her new grandmother-in-law, before officially opening the Mersey Gateway Bridge in Widnes and the Storyhouse cultural centre in Chester.
It is believed that Meghan may have offered to let the 92-year-old go before her so that she was best positioned to exit on the pavement side when the vehicle comes to a stop. Meghan then climbed in first. "I have a feeling she's going to push the limits a little too much?!"
Queen Elizabeth, the world's longest-reigning and oldest monarch who has carried out thousands of engagements during her 66-year reign, appeared at ease with the newest member of the Windsors.
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The swish Royal Train has nine carriages and Meghan will stay in one of the ensuite bedrooms, and dine in the 12-seater dining room.
They were then able to replenish themselves by enjoying a lunch at the town hall.
Stalls selling flags and souvenirs have set up on the streets of Chester and schoolchildren who will meet the Queen and duchess during the day were delivered to where they needed to be early this morning.
This can be shortened to Mama, when Meghan gets to know her as Diana did.
The pair were pictured smiling and laughing as they opened the Mersey Gateway Bridge, a new toll bridge over the River Mersey and one of the UK's biggest infrastructure projects in recent years.