Some time ago this subject came up in Eng-Tips, but like normal I can't find it! A nice solution was to insert a standard rectifier diode in the current path, and connect a mA meter across the diode when a reading was required. Provided the meter burden drops less than about 0.5V when passing the current, the diode isn't even thinking about conducting so the current measurement is accurate, and there is no requirement to break the loop for testing.
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One day my ship will come in.
But with my luck, I'll be at the airport!