There are two things which can be done to minimise the effect of PN junctions:
1) Use as lower test voltage as possible, preferably lower than a diode drop. Lots of modern multimeters do this. I've just tested my Amprobe 37XR with a cheap meter with a 1M input impedance and it reads 40mV. I think the higher resistance ranges use a lower test current/open circuit voltage because a known good 1N4148 reads open circuit.
2) Measure the resistance in both directions and record the higher value, which will be the one when the diode reverse biased.
If there's a small voltage on the circuit, which doesn't cause the meter to read open circuit, then measure the resistance with the probes connected in opposite polarities and take the average of the two readings. Another option, assuming it can be safely short circuited, is to measure the open circuit voltage and the current, when short circuited, and calcualte the resistance using Ohm's law: R = V/R. Obviously it's normally a bad idea to measure the resistance when there's a voltage present, but sometimes it's a necessary evil.