Let's say I have a closed, non-transparent metal container with pressurized gas and I'd like to measure the pressure inside without changing that pressure (or changing it as little as possible).
The thickness of the (metal) container walls isn't known, and there is no replica of it you could take apart to measure that; for example it may be a military tamper-proof device with a pressure sensor in the middle that destroys valuable data if that pressure changes, so the only way to "defuse" it would be to open it in a room which pressure is as close as possible to the box's pressure.
The gas in the container has no special properties and is only designed to keep that pressure; nitrogen gas seems to be a plausible option.
The sensor of course isn't perfect and has to leave a tolerance margin for vibrations and temperature changes, however we shouldn't rely on that and if possible the measurement shouldn't change the pressure at all.
There is a similar example on the Wikipedia page for the observer effect, but it's just a short example and a search for measure pressure observer effect doesn't find anything relevant. This similar question - Find pressure of liquids without making contact with it - is only about liquids and the answers suggest to look at the quantity of liquid inside to estimate its quantity, however for a compressible gas that doesn't seem possible.