In contrast to the demands for the hardware emulation of existing resistive switching devices with complex nonlinear dynamics, most of today's hardware emulators mimic the behavior of ideal memristors, which comply with original Chua's definition. We demonstrate an effective method of emulating complex models such as the models by Pickett, Bayat, or Strachan. All these devices can be modeled as first-order extended memristors with their standard port and state equations. The core of the emulator consists of a microcontroller-based nonlinear resistive two-port. One port is supplied from a current source controlled by a nonlinear function of the voltages across both ports. The state equation of the emulated device is modeled via connecting a capacitor across this port, its voltage being a state variable. The second port is loaded by a digital potentiometer whose conductance is controlled by port voltages. This port implements the equation of state-dependent Ohm's law. The digital potentiometer, as well as the microcontroller providing the digital signal processing of the port and state equations, are carefully selected in terms of the dynamic range, quantization noise, speed, complexity of modeled equations, and power consumption. The emulator was successfully tested for mimicking the complex behavior of the above devices in fully floating configurations.