Electrogenic cells such as cardiomyocytes and neurons rely mainly on electrical signals for intercellular communication. Microelectrode arrays (MEAs) have been developed for long-term recording of cell signals and stimulation of electrogenic cells under low-cell-stress conditions, providing new insights in the behavior of electrogenic cells and the operation of the brain. To date, MEAs are relying on flat or needle-shaped electrode surfaces, mainly due to limitations in the lithographic processes. This paper relies on a previously reported elasto-capillary aggregation process to create 3D carbon nanotube (CNT) MEAs. This study shows that CNTs aggregate in well-shaped structures of similar size as cardiomyocytes are particularly interesting for MEA applications. This is because i) CNT microwells of the right diameter preferentially trap individual cardiomyocytes, which facilitates single cell recording without the need for clamping cells or signal deconvolution, and ii) once the cells are trapped inside of the CNT wells, this 3D CNT structure is used as an electrode surrounding the cell, which increases the cell-electrode contact area. As a result, this study finds that the recorded output voltages increase significantly (more than 200%). This fabrication process paves the way for future study of complex interactions between electrogenic cells and 3D recording electrodes.