While watching a performance by local schoolchildren, the pair were seen chatting excitedly and making whispered remarks to one another. Neither Meghan nor Her Majesty could suppress their laughter at certain moments.
The former actress and Her Majesty travelled to Chester aboard the Royal Train on Wednesday night, arriving at Runcorn Station on Thursday morning.
Meghan's invitation to travel on board with Queen Elizabeth II was a rare privilege that made royal history. No other young royals have ever travelled alongside the Queen on the train overnight for a royal engagement - including Kate Middleton, Prince William and Prince Harry.
Meghan opted to wear an beige caped dress by Givenchy, while the Queen stood out from the crowds in a vivid green coat.
They were accompanied by Samantha Cohen, the Australian-born royal adviser who was recently appointed Prince Harry and Meghan's private secretary.