Is there a practical way to increase the input impedance of an instrument?
The classic articles on dealing with high impedance have got to be Bob Pease's "What's All This Stuff" series. Try this and this for a practical starting point.

And, by the way, measuring resistance does not usually require a high input impedance, since a current-to-voltage converter is norm, and a transimpedance amp is the way it's usually done. Low leakage, yes: low input impedance, no.