Considerable attention has been recently given to electromagnetic resonant shunt tuned mass damper-inerter (EH-TMDI) for simultaneous vibration mitigation and energy harvesting. However, only linear structures have been investigated. Hence, in this paper, we aim at simultaneously achieving vibration mitigation and energy harvesting for nonlinear oscillators. To do so, we attach a nonlinear electromagnetic resonant shunt tuned mass damper-inerter (NEH-TMDI) to a single degree of freedom nonlinear oscillator (Duffing Oscillator). The nonlinear oscillator is coupled to the tuned mass damper via a linear and a nonlinear spring. Both the electromagnetic and the inerter devices are grounded on one side and connected to the nonlinear vibration absorber on the other side. This is done so to relax the trade off between energy harvesting and vibration suppression. The electromagnetic transducer is shunted to a resistor-inductor circuit. The governing equations of motion are derived using Newton’s method. Numerical simulations are carried out to examine the performance of the proposed NEH-TMDI. Comprehensive parametric analyses are conducted to identify the key design parameters that render the best performance of the NEH-TMDI. The results show that selected parameters offer regions were maximum energy dissipated and maximum energy harvested coincide. The findings are very promising and open a horizon of future opportunities to optimize the design of the NEH-TMDI for superior performance.