As the leader of the Polish delegation to the Council of Constance (1414–1418) (along with Andrzej Łaskarz, Jakub z Korzkwi Kurdwanowski, Paweł Włodkowic and Zawisza Czarny), he was part of the larger German delegation. After they arrived in Konstanz in 1415, Trąba was, according to Ioannes Longinus, briefly considered as one of the candidates for papacy, although historians still debate the reliability of this information. Certainly Trąba temporarily abandoned his support for the Polish cause, supporting pro-Teutonic candidate Oddone Colonna, the future Pope Martin V against pro-Jagiełło Antipope John XXIII. This would later cause him problems in Poland, as well as his lack of criticism of the sentence on Jan Hus, which caused further questions about his loyalties in Poland and Bohemia, especially when contrasted with strong defence of Hus by Włodkowic.