Exposure systems have been reported to deliver high-intensity nanosecond pulsed electric fields to biological cells and simultaneously observes the induced biological effects. However, there is a lack of measurement techniques for characterizing the macroscopic electric field and microscopic temperature changes induced inside the exposed sample. In this paper, we present dosimetry measurements at macroscopic and microscopic scales inside a Petri dish containing biological cells and exposed to nanosecond electrical stimuli within a transverse electromagnetic cell.