Simulating an Old Vacuum Sensor
It seems unclear what the configuration is and how it works. Presumably some kind of differential arrangement. Perhaps an LVDT or RVDT as suggested above.
An LVDT arrangement typically has at least 4 wires and three coils. The inductance is not directly used in an LVDT arrangment. There is one pair of wires that excites the LVDT and the other pair picks off the output.
If it is an LVDT, the task is to measure the excitation voltage and produce an output voltage that is linearly proportional to the desired output (usually signed, so 4-quadrants). That's pretty much just a 4-quadrant analog multiplier. Typically LVDTs are excited by signals in the kHz range, which is not difficult for a multiplier chip to handle. You would need a bipolar DAC to produce the control voltage.
It could be done all digitally, of course, but you'd need an ADC then and a reasonably fast processor.
Edit:
Possibly could be done with a relatively high voltage digital pot and bipolar power supplies. Some measurements of the voltages and currents would be required. At least an oscilloscope! And a working unit.