According to Diário de Notícias da Madeira, the couple was last seen at 3:45pm yesterday on Avenida Marcos Marques Rosa in Sítio do Calhau, walking towards Porto Moniz.
The couple was staying in Fajã da Areia and the alert was probably given by their daughter.
A PSP source confirms that the searches will continue this Monday, according to press reports.
The man, who is 1.80m tall, was wearing a grey jacket and loose blue tracksuit trousers and the woman, who is 1.69m tall, was wearing a blue sports coat and carrying a pink backpack.