The Cambridge Face Memory Test Long (CFMT+) is used to investigate extraordinary face recognition abilities (super-recognizers [SR]). Whether lab and online presentation of the CFMT+ lead to different test performance has not yet been investigated. Furthermore, we wanted to investigate psychometric properties of the CFMT+ and the Glasgow face matching test -- short (GFMT-S). We report item difficulties, Cronbach's Alpha, and T norms for the CFMT+ and GFMT-S depending on the presentation mode. We analyzed variations of CFMT+ and GFMT-S performance by means of presentation mode, age, and gender. The results showed significant better CFMT+ performance for online presentation, women, and participants between 26 and 35 years of age. For the GFMT-S, significantly higher test performance was shown for online participants exclusively. Overall, we discuss the modulating effects of participants' motivation for online assessments, the necessity of differential norms (e.g., for personnel decisions), and the application of T norms.