At the 1936 Summer Olympics, she logged the competition's second-highest optional balance beam exercise[4]: 402  score of 14.10, tied with Germany's Erna Bürger, and only behind top-scorer Gabriella Mészáros of Hungary.

At the 1948 London Summer Olympics, she performed even more brilliantly in her voluntary exercise on this apparatus, garnering a first-place finish for that part of the competition.

At the first-ever world championships for women in 1934, where individual and team placements were decided not only by gymnastics events, but also athletics events, in the gymnastics-events-only segment of the competition, she logged the 2nd-highest total of 30.85,[2] ahead of even her teammate, the first-ever women's World All-Around Champion in the sport Vlasta Děkanová, and just behind Judit Tóth of Hungary.

Veřmiřovská actually repeated the feat of defeating Děkanová when, incredibly, both still competing after World War II, they were the top 2 competitors at a domestic (Czechoslovakian) gymnastics competition held on 6 October 1946.

Dozens of participants competed, including 3 individuals who were on the Olympic team less than 2 years later: Miloslava Misáková, Olga Šilhánová, and Věra Růžičková, all outscored by many percentage points by both Veřmiřovská and Děkanová who were in a class by themselves, despite both being well into their thirties.