The purpose of the research was, with the aid of a short questionnaire, to determine how postgraduate students (N = 32) perceive the opportunities for creative research in general, and how they perceive creativity in the preparation of their own research work in particular. Descriptive analysis shows that students (1) perceive a positive study-research climate that encourages creative processes (independence, motivation, intellectual challenges); (2) judge that researchers have numerous opportunities for creative work in the various phases of research; and (3) evaluate themselves as highly creative individuals in everyday life. Students perceive themselves as being at their most creative in the definition of the research problem, which they mainly identify with the use of personal strategies (work experience) and take various lengths of time to form, typically up to one year. The most difficult problem in this regard is represented by giving meaning to the problem (breadth, depth, specificity, application). Amongst the perceived encouragement with which mentors motivate students for creative research the most frequent is less directive general guidance in study and research. On the basis of the presented findings, guidelines are suggested for the more effective encouragement of creative research in postgraduate students.