Research has revealed that teachers find teaching and assessing socioscientific argumentation (SSA) to be challenging. In this study, ten pre-service science teachers (PSTs) tested a new Practical Assessment of Socioscientific Argumentation Model (PASM) that was developed to enhance skills in assessing SSA. The models' design is based on the Teacher oriented Assessment Framework. Here, we present the characteristics of PASM and examine how PSTs perceive that the use of PASM effects competences in assessing SSA. PASM is divided into multiple phases and requires PSTs to perform three roles: arguing for and against a given socioscientific issue, and assessing other PSTs' argumentation. It also includes group discussion and individual reflection phases. Two cycles of the model were performed, focusing on different issues (GMOs and nuclear power). Data were collected in the form of audio-recordings of group discussions, field notes from whole class discussions and the PSTs' written individual reflections. Thematic data analysis revealed that the PSTs discussed and reflected on four main themes: the focus of the assessment, the tools in PASM, the nature of PASM, and coping strategies. The nature of PASM, with iterative cycles and repeated reflections, expanded their views on assessing this kind of argumentation, making PSTs aware of quality criteria that should be included in assessment of SSA. We conclude that it is important to include training on assessing SSA in teacher education and that PASM could be a valuable tool for this purpose.