A growing interest has been observed among K-12 school educators to incorporate maker pedagogy into science, technology, engineering, and mathematics (STEM) education to engage students in the design and making process. Both cognitive engagement and emotional engagement of students can be promoted through satisfying the psychological need of relatedness that concerns a sense of connection and belonging. How to support relatedness would influence the effective development of students’ cognitive competencies, namely creativity and critical thinking, and non-cognitive characteristics, namely interest and identity. Therefore, the present study investigated how two relatedness support strategies—real-world problems (RWP) and mentoring influence the development of student’s STEM-related cognitive competencies and non-cognitive characteristics in STEM marker activities. We implemented a 7-week intervention study with three classes of Grade 9 students (aged 13–15 years) in Hong Kong (n = 95). Three intervention conditions were designed in the experiment, comprising textbook problem (TBP), RWP, and RWP with mentoring (RWPM). Our analysis showed that (i) the differences in creativity among the three groups were non-significant, (ii) the RWP and RWPM groups showed stronger critical thinking than the TBP group, and (iii) the RWPM group exhibited stronger STEM interest and identity than the other two groups. This study revealed the effectiveness of adopting RWP strategy in developing secondary students’ perceived cognitive competencies (e.g., creativity and critical thinking) and the feasibility of employing a mentoring mechanism for cultivating learners’ perceived non-cognitive characteristics (e.g., STEM identity and interest). Hence, we also offered practical suggestions for teachers.