By the mid-1920s, she had largely abandoned painting and concentrated on graphic art: drawing, and printmaking in mezzotint, drypoint, aquatint, woodcutting, and monotyping.

[4] In 1927, she accompanied her husband, painter Kuno Veeber, to Venice on a grant he received from the Estonian Cultural Endowment Fine Arts Foundation to copy works by the Old Masters.

Early graphic pieces from Veeber include portraits, monuments, and cityscapes (several drawings and prints of Tallinn's St. Nicholas' Church) in peaceful and meditative black and white tones.

[8][9] Shortly after arriving in the United States, Veeber illustrated the first edition of Estonian author and fellow exile Henrik Visnapuu's 1948 novel Mare Balticum.

Veeber's oeuvre while in exile in the U.S. became more stark; the black and white prints were often more rough and jarring than her prior work in Estonia and explored nature motifs, harbor cities and animals.

Veeber also continued to exhibit throughout her life, with personal exhibitions at the Columbus Museum of Art (1960); the Estonian House in New York (1961, with Arno Vihalemm); the Peetri Church Hall of Toronto (1963, with Endel Kõks [et]), and the Art Museum of Estonia at Kadriorg Palace (1984).