To clarify, even the quality of the probes and clips really doesn't matter at this level.
Consider a 5V reference connected to a 10M Ohm input DMM. Current flow is 0.000,5mA. Add 10 Ohms to that circuit to represent a very bad connection and the voltage drop is only 0.005mV. So you would need a 5 million count or better DMM to even see this (typically a 7.5 digit DMM). If your DMM has a > gig Ohm input option at this voltage, then it truly doesn't matter.
Consider a 1mA current source from the DMMCheck Plus, which in my sample maxes out just above 500mV. The resistance in the circuit would have to exceed 500 Ohms before it would not be able to generate 1mA. Common DMM shunt resistances are around 2 Ohms for mA and 100 Ohms for uA. Again in this case, adding 10 Ohms for a bad connection will not make any difference.