This paper presents the design and calibration of seven new Rogowski coils, namely, three air-cored coaxial-cable wound coils (RC1-RC3), one ferrite-cored varnished-wire wound coil (RC4), and three air-cored varnished-wire-wound coils (RC5- RC7). All coils are wound in a single layer and operated in the self-integrating mode, especially RC1-RC4. RC5-RC7 are mainly operated in the differentiating mode with external passive integrators. The designed seven coils are calibrated using different impulse currents up to 8.5 kA. These currents are simultaneously measured by different methods, namely, an impulse current transformer and a commercial Rogowski coil (ICT and CRC, respectively). Winding pitch advancement errors and magnetic fields into the plane of the coil are compensated by using a one-turn return loop placed inside the helical winding in the opposite direction to the pitch advancement for all coils except for RC4. It is found that all designed coils have a constant sensitivity of 0.2-4.4 V/kA over a certain bandwidth up to few MHz and with a very low sensitivity phase angle. For the self-integrating coils (RC1-RC3), increasing the number of turns and/or the former size enhances the coil response. For the differentiating coils with external integrators, the higher the integrator resistance and/or capacitance, the better the response (less droop effect and time shift) and the lower the sensitivity. The optimized termination resistance for the self-integrating coils and the integrator parameters for the differentiating coils enables the currents measured by RC3, RC4, and RC6 to have excellent agreement with those measured by ICT and CRC for different loads and levels without any droop effect.