I've done it on a test bench with a Yokogawa GS200 voltage-current source (the older 7651 also works, and the ADCmt 6146 probably will too), an oscilloscope and a current probe (a shunt resistor is sufficient).
Set the GS200 for a sweep, whatever voltage range you want. Make the sweep fairly quick, a few hundred milliseconds. Depends how many steps you need really.
Set scope for X-Y. X axis is voltage across the component. Y axis is current.
If you can't get your hands on a GS200, DIY a ramp generator or sine oscillator and a power amplifier to replace the GS200. If you have a function generator, use it and build a power amp for it. Couple of opamps, a gain pot and a Class-AB output stage.
If you want to do better, use a high-gain instrumentation amp and a low-value current shunt resistor to reduce burden voltage in the current sense stage.
You could probably DIY most of this into a self-contained measuring instrument for not a lot of money. There was an old Maxim/Dallas appnote which explained how to turn a PC with a parallel port into an I-V curve tracer. It was as slow as molasses, but it worked reasonably well.