This popular beach gets its name from the Palace of the Dukes of Palmela (Palacio do Duque de Palmela) which overlooks it. Along with adjoining Praia de Conceição, this is the most easily accessed beach from Cascais town and the train station. As such it can get pretty busy in the summer months.
At lower tides Praia de Duquesa and Conceição beaches join together to form one sandy stretch. As the tide comes in they are separated by the Faial Chalet the former Court of Justice for Cascais province, however you can still walk between the two beaches on the Estoril-Cascais coastal promenade.