As the royal party stood on a platform, London Underground chief operating officer Howard Collins made the presentation of the white badge printed with the words "Baby on board" and featuring the famous London Underground roundel.
Watching guests laughed as Mr Collins handed over the gift and Kate held it against her teal-coloured Malene Birger coat and joked "I'll make sure I wear it at home".
Mr Collins said afterwards: "Kate said 'Oh yes, I've seen this before'. She used to travel on the Tube so she probably saw them then.
"She asked me 'How do they work?' and I said they're fantastic, they really do make a difference - saves men the embarrassment of having to guess if a woman is pregnant. She asked so many great questions of the staff and seemed really interested in our work."
The badges, available from Transport for London (TfL), overcome the awkwardness often felt by pregnant women of having to ask someone to give up their seat.