One issue is with measuring small capacitance, any coupling between the leads can create errors. Also if the cables move, bend, or change position this can create a change in the setup residual capacitance and corrupt measurements. Having each individual wire shielded reduces the coupling IF the shields are terminated. These are reasons mentioned for using a rigid mechanical fixture for small capacitance readings where things are fixed and don't move.
Another issue is potential EMI susceptibility, where shields help reduce the actual external signal coupling onto the inner signal lead, although most DMMs have pretty good EMI filtering since they are designed to work with unshielded cables/probes.
With high valued resistance measurement leakage can corrupt measurements, and having shields terminated helps keep the leakage current controlled and confined, in some cases the shield can act as a
"guard" where the shield is driven by a voltage similar to the one on the conductor the shield is guarding. This reduced the differential voltage between the inner lead and shield and reduces leakage. This very technique was employed eons ago to effectively reduce the cable capacitance as "seen" by the signal on the cable inner conductor, since displacement capacitive current is proportional to dV/dT, by making dV~0, or shield voltage approximately equal to the conductor signal (unity gain buffer amp to drive the shield), then the displacement current is reduced and capacitance as "seen" by the conductor signal is reduced. We patented a 2 dimensional similar technique to reduce the electron leakage between adjacent pixels in an ultra-sensistive night vision imaging chips (patent 8102452), this is where every electron counted!!
Anyway, I'm sure 2N3055 and others can elaborate much more on this issue as we're certainly no expert on this.
Edit: That's a great article mentioned by Someone, must read

Best,