The HP 3575A is a "relatively compact boat anchor", beautifully made, that will do 1Hz - 13Mhz according to the specs and they go for real cheap on eBay.
You drive it with your existing signal generator and it displays the gain and phase between its two ports. You can get the data out the back of it through an analog voltage that you can log on a scope for Bode plots etc.
It is definitely able to characterise components like resistors, electrolytics, inductors, etc. as long as you don't need sub-PPM results... think 1970's Pontiac GTO with a 455 with functional ram air intakes on the hood, rather than a Porsche, Audi, or BMW, and you get the idea!