The first methods described by Analog Ground will still work, even at 1mA. You will just get less accuracy. But no measurement is perfectly accurate. So you have to specify how much accuracy you need. In general, the accuracy of the Analog Ground method depends on the applied voltage. The more that voltage exceeds the nominal 0.7 v. diode drop, the better the accuracy. Whether that can be achieved with only 1 mA depends on the range of resistors that could be in series with the diode. If the resistor is around 20K, for example, then 1mA of current will generate 20v across the resistor, which is much more than the 0.7v across the diode. Therefore we can say we have effectively taken the diode out of the consideration, to within about 5%. So you could measure the voltage at 1 mA and the voltage at 0.5 mA, divide the difference between these two voltages by 0.5 mA and get a fairly good approximation to the unknown resistor. On the other hand, if the resistor is in the range of 10 Ohms, then 1 mA will only produce about 10 mV, which is swamped by the 700 mV across the diode. So it will be very difficult to make any kind of estimate of the resistor if the resistor were in that range.