Electrical Meter Basics
The key to measuring a 4-20mA signal is realizing that it is a current signal so to measure it, your meter must become part of the loop.
People typically blow the fuse in their meters when measuring a 4-20mA signal by connecting the meter across the circuit (in parallel) instead of in series.
To correctly measure current (like 4-20mA), the meter must be inserted into the circuit, acting as part of the loop. If you connect it in parallel, you essentially create a short circuit, allowing a much higher current than the meter's fuse is rated for to flow through it, causing the fuse to blow.
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