The first one is a Heart Vase (Hjertevase in Danish) from the 1955-designed 'Menuet' range. The signature on the bottom is the date it was made (1957), and in the middle is Per Lutken's 'PL' monogram.
The second piece was designed by Christer Holmgren. The signature on the bottom, HG4, means it was made in 1974, although design dates to c.1969, as it appears in the Kastrup-Holmegaard catalogues, as well as the later Holmegaard ones. It is design number 13 09 49 in the Kastrup-Holmegaard trade catalogues, and became design 341 45 17 in the post-1970 Holmegaard catalogues. There won't be any more signature under the label.
Image from the 1969 Kas-Holm catalogue...