This is foolproof technique.
1) Immerse the stuck vessels in water by adding weight into vessel, anything heavy.
2) After water goes into the lower vessel, heat it on a flame, dry heating.
3) The water in the lower vessel evaporates. The steam pushes the upper vessel.
4) The vessels are thus separated effortlessly without causing any damage to the dishes.
Source: Mother's experience.
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One of the children (possibly the one named "not me") had nested two of my pots and they have become stuck together.
How do you separate two pots that were put together to form a double boiler?