There are more things in heaven and earth, d'alar'cop, than are dreamed of in your philosophy.
Uniqueness is tough. One of the chief devices used in riddling is metaphor. This guarantees non-uniqueness, in a sense, because the whole point of a metaphor is that two or more different things share certain properties. Because figurative language is another given in riddles, the interpretation of the metaphor is broadened further.
The idea is to use as many different figurative or metaphoric descriptions as are necessary to ensure that the intersection of their interpretations is a single word or phrase.
How do you achieve this, or better, how do you know when you have achieved this? In practical terms you can't. To be sure, you would have to map all of the words in the riddle's target language to all the possible interpretations of the riddle's statement and verify that the cardinality of the result is one.
If you look carefully at nearly any of the classic riddles, are they 100% solid? Are they a 100% fit? No. They may be good, they may be satisfying but are they rigorous (I assume this is what you mean by "solid")? Probably not.
Language is notoriously imprecise. Word meanings drift. "Solidity" is very difficult to achieve. I, myself, have tried to end-run the problem by constructing riddles that describe both the form and the content of the answer. I give some more or less metaphorical descriptions of the subject as in the classical riddles but I also give one or more clues such as you would find in cryptic crosswords. You can attack them from whichever end appeals to you most and use the other to verify your answer. Cryptic clues are a pretty good path to uniqueness.
I have had a number of artistic failures but with this method but I believe I have done fairly well in regard to being "solid". I cannot claim originality, by the way, a number of riddles of this type can be found in Jane Austen. Probably elsewhere as well but that's where I got the idea.