Part of the answer depends on what you are using to do the measurements with, a DVM has different characteristics from a resistance bridge. To some degree, the values of resistance also come into play, on average high values tends to be much more susceptible to noise pickup than low values. The two main sources I contend with using my resistance bridge is static fields and small emf values and with high values, particularly >1Meg, some types of noise can cause (such as lighting) wavering nulls. With a resistance bridge most effects that interfere with a reading tend to be self evident and as it is a differential device, it tends to reject a lot of noise. That said, in making very precise measurements, you still have to be careful to pay attention to any possible sources of error, some can be very 'sneaky' and not so easy to see.
While DVMs are sampling devices that 'average' the input over a period of time, that can help with certain types of noise (Gaussian) but not all noise sources can be averaged out. While higher resolution DVMs have 4-terminal resistance measurement which can minimize certain error sources, it is not free of errors by any means. It is also susceptible to outside error sources such as static fields, relatively high EMI fields and even EMF to some degree. A DVM can be even more sensitive to noise pickup with high value resistors than a resistance bridge, this may appear as 'dancing' digits or perhaps just an offset from the actual value.
In any case, external noise fields should be eliminated or minimized for best measurement accuracy, it is easier to eliminate noise at the source than to try and filter it out, most DVMs will have a guard terminal as do high end resistance bridges, this is very helpful to use for shielding purposes. Leads should be kept as short as possible, long leads invite trouble, copper leads should be used (not plated) and for high accuracy, banana plugs should be avoided as they introduce unknown contact resistance and possible noise into the circuit. Keep all terminals at the same temperature to minimize EMF and keep them the same length. Kelvin clips can make very good connections to the unknown resistor if done correctly. There are a lot of sources of error in precision measurements, any number of them can bite you and you might not even know they are there, experience is a good teacher.
Be aware that shielding increases capacitance and can affect settling time of the measurement, sometimes noise can even be injected into the measurement from the shielding, nothing is perfect, you can only minimize at best, with practice you can achieve very good accuracy and find your limits....don't make assumptions, that is the path to making errors, don't assume your measurements are as accurate as you think they are unless verified by a credible source, calibration is very important for accuracy.