Managers who select projects have a moral responsibility. The purpose of this paper is to present a template to assess this responsibility so that it can be put into practice. Responsibility is here defined as a combination of attributability—what choices the project manager can ultimately be praised or blamed for, and of accountability—what choices the project manager has to be prepared to answer for. The template combines these two aspects of responsibility with the project selection process divided into three phases: initialization phase, appraisal phase, and decision phase. Various moral philosophers are used to highlight the moral issues at stake for each of these two dimensions of responsibility at each stage of the project selection process. Concluding remarks underlines the need for project selectors to adapt to the specific context when they use the template.