Students' social belonging in introductory science, technology, engineering, and mathematics courses has repeatedly been shown to be an important influence on students' outcomes in these courses. Previous studies have further identified students' sense of belonging and belonging uncertainty as related but unique components of their broader social belonging that can independently affect outcomes. High belonging uncertainty (doubts about the quality of one's social connections or academic ability in a course) may particularly disadvantage historically marginalized groups in physics, such as women or students of color who face negative stereotypes based on their identity. Additionally, high-stakes exams, such as traditional final exams in introductory physics classes, can disproportionately disadvantage historically marginalized groups. In this study, we investigated the effect of social belonging on students' performance across two Introductory Physics 1 sections with two variations of final assessment: one section that took a traditional final exam and one section that completed a nontraditional final course project. Both assessment types were high stakes and constituted a similar, substantial proportion of students' final course grade. We found that both students' sense of belonging and belonging uncertainty impacted their final assessment score, regardless if they took the traditional final exam or completed the nontraditional final project. The findings of this study illustrate how students' social belonging can impact performance even on nontraditional assessments if such assessment is of similar high stakes to a traditional exam.