Transversal skills (TS) are fundamental to both work effectively autonomously and with others in society. They are key to educating responsible engineers able to assess and proactively respond to issues and opportunities. As evidenced by recent course syllabi and accreditation requirements, TS are increasingly integrated in engineering curricula. However, little is known about students' perceptions of key pedagogical aspects related to skill development and the TS they prioritise. In light of previous work showing that demographics can influence students' perception of curricular experiences, this study reports on perceptions of 244 students on how TS are integrated into their programmes based on demographic information (discipline, year of study, gender) and participation in curricular activities (internships, mentoring programmes). Our data showed that students perceived low levels of receiving information and assessment, and even lower levels of receiving feedback related to TS. Open questions about the skills they most wanted to develop and which they received least support did not reveal major trends in relation to either curricular experiences or demographic characteristics. This lack of major trends is however a positive result, as it points to reasonably equitable experiences for students in the institution. So, while this study supports the importance of increased attention to developing TS, it also raises questions about how to interest and support students to develop robust TS and therefore prepare them to be responsible engineers.