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Understanding neural mechanisms in design and creativity processes remains a challenging endeavor. To address this gap, we present two electroencephalography (EEG) datasets recorded in design and creativity experiments. We have discussed the details, similarities, differences, and corresponding cognitive tasks of the two datasets in the following sections. The design dataset (Dataset A) comprises EEG recordings of 27 participants during loosely controlled design creation experiments. Each experiment included six design problems. In each design problem, participants performed five cognitive tasks, including problem understanding, idea generation, rating idea generation, idea evaluation, and rating idea evaluation. The NASA Task Load Index was used in rating tasks. The creativity dataset (Dataset B) includes EEG signals recorded from 28 participants in creativity experiments which were based on a modified variant of the Torrance Test of Creative Thinking (TTCT-F). Participants were presented with three incomplete sketches and were asked to perform three creativity tasks for each sketch: idea generation, idea evolution, and idea evaluation. In both datasets, we structured the experiments into predefined steps, primarily to ensure participants' comfort and task clarity. This was the only control applied to the experiments. All the tasks were loosely controlled: open-ended (up to 3 min) and self-paced. 64-channel EEG signals were recorded at 500 Hz based on the international 10-10 system by the Brain Vision EEG recording system while the participants were performing their assigned tasks. EEG channels were pre-processed and finally referenced to the Cz channel to remove artifacts. EEGs were pre-processed using popular pipelines widely used in previous studies. Preprocessed EEG signals were finally segmented according to the tasks to facilitate future analyses. The EEG signals are stored in the .mat format. While the present paper mainly addresses pre-processed datasets, it also cites raw EEG recordings in the following sections. We aim to promote research and facilitate the development of experimental protocols and methodologies in design and creativity cognition by sharing these resources. There exist important points regarding the datasets which are worth mentioning. These datasets represent a novel contribution to the field, offering insights into design and creativity neurocognition. To our knowledge, publicly accessible datasets of this nature are scarce, and, to the best of our knowledge, our datasets are the first publicly available ones in design and creativity. Researchers can utilize these datasets directly or draw upon the considerations and technical insights provided to inform their studies. Furthermore, we introduce the concept of loosely controlled cognitive experiments in design and creativity cognition. These experiments strike a balance between flexibility and control, allowing participants to incubate creative ideas over extended response times while maintaining structured experimental sections. Such an approach fosters more natural data recording procedures and holds the potential to enhance the accuracy and reliability of future studies. The loosely controlled approach can be employed in future cognitive studies. This paper also conducts a comparative analysis of the two datasets, offering a holistic view of design and creativity tasks. By exploring various aspects of these cognitive processes, we provide an understanding for future researchers.