User experience (UX) has become an important aspect in the evaluation of interactive systems. In parallel, conversational interfaces have been increasingly used in many work and everyday settings. Although there have been various methods developed to evaluate conversational interfaces, there has been a lack of methods specifically focusing on evaluating user experience. This study reviews the six main questionnaires for evaluating conversational systems in order to assess the potential suitability of these questionnaires to measure various UX dimensions. We found that (i) four questionnaires included assessment items, in varying extents, to measure hedonic, aesthetic and pragmatic dimensions of UX; (ii) two questionnaires assessed affect, and one assessed frustration dimension; and, (iii) enchantment, playfulness and motivation dimensions have not been covered sufficiently by any questionnaires. We recommend using multiple questionnaires to obtain a more complete measurement of user experience or improve the assessment of a particular UX dimension.