Researchers and policy-makers have recognized the importance of including and promoting socioscientific argumentation in science education worldwide. The Swedish curriculum focuses more than ever on socioscientific issues (SSI) as well. However, teaching socioscientific argumentation is not an easy task for science teachers and one of the more distinguished difficulties is the assessment of students’ performance. In this study, we investigate and compare how science and Swedish language teachers, participating in an SSI-driven project, assessed students’ written argumentation about global warming. Swedish language teachers have a long history of teaching and assessing argumentation and therefore it was of interest to identify possible gaps between the two groups of teachers’ assessment practices. The results showed that the science teachers focused on students’ content knowledge within their subjects, whereas the Swedish language teachers included students’ abilities to select and use content knowledge from reliable reference resources, the structure of the argumentation and the form of language used. Since the Swedish language teachers’ assessment correlated more with previous research about quality in socioscientific argumentation, we suggest that a closer co-operation between the two groups could be beneficial in terms of enhancing the quality of assessment. Moreover, SSI teaching and learning as well as assessment of socioscientific argumentation ought to be included in teacher training programs for both pre- and in-service science teachers.