They wore contrasting colours, the duchess choosing a beige Givenchy pencil dress and the queen in a lime green coat-dress and matching hat.
The Queen, 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. It was to be followed by events including the unveiling of a plaque to officially open the Mersey Gateway Bridge.
The awkward exchange comes as Meghan continues to adjust to life as a full-time royal.
"The role that she's taken on it's very austere, it's very sort of serious and I think there's a great weight that she has. acquired through that and she takes it very seriously", she said.
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The only time the ball was in midfield was when it was passing through to either end, with the teams combined for 18 shots. Hernandez and Vela drive forward but the former overcooked his pass and allowed Kimmich to recover and clear the danger.
The Duchess of Sussex at first called the Queen "Your Majesty" before curtseying while out on a trip in Cheshire.
The decision by Queen Elizabeth, 92, to invite the Duchess to join her - less than a month after her wedding to Prince Harry - shows the royal family has no hesitation in using the confident and poised Meghan for public appearances.
The Queen walked down one side of the road and Meghan the other as they stopped to chat to people and collected dozens of floral bouquets and other gifts.
They arrived in Cheshire onboard the royal train and are visiting the new Mersey Gateway Bridge and Chester.
Next on the agenda is a medley of songs from the Storyhouse's latest production A Little Night Music, and then they will see local schoolkids perform songs with actors from Swallows and Amazons.