A Wheatstone bridge can measure high resistances, but accuracy diminishes due to current limitations through the resistor being tested. The challenge arises when trying to detect a zero balance point, as the current may be too low for precise readings. Solutions include using amplifiers or replacing the galvanometer with a low-offset op-amp to improve measurement capability. For resistances around 10^8 ohms or higher, specialized equipment like a low input bias current transimpedance amplifier or instruments from Keithley Instruments is recommended. Overall, while a Wheatstone bridge can be adapted for high resistance measurements, it requires careful consideration of its limitations.