She finished off her look with a pair of velvet Jimmy Choo heels (another Meghan staple) and crystal embellished hoop earrings.
The Duchess, who became the first Royal Patron of the museum in March this year, toured the opening exhibition Collecting Photography: From Daguerreotype to Digital which showcased photography dating back from its invention in the 19th century to present day.
William and Kate have always been involved in mental health initiatives through their Heads Together campaign.
Kate only returned to royal duties last week after taking maternity leave for the birth of the couple's third child Prince Louis.
"Where can you hide it", Kate joked as she painted a white stroke, and which point Prince William said, "It's nearly ruined the picture", before adding, "No, this is probably how you ruin a picture" as he took his turn.
She has expressed her love for photography and has taken portraits of her children Prince George and Princess Charlotte in the past.
They also heard presentations on two case studies of active mental health programmes from Slovenia and the US and visited an exhibition area.
The Duke and Duchess viewed the work of contemporary fine artist Dario Vargas, who had painted an original piece for the event.
Erdem is a much beloved designer of the royals, with speculation around whether the brand has designed Princess Eugenie's wedding dress for her nuptials on Friday.