Brazilian here. I honestly don’t get the idea of the pretense uniqueness of the term “saudade”. Sure there is not an equivalent noun in English, but, to me, the verb “to miss” someone or some place conveys precisely the same feeling.
> the verb “to miss” someone or some place conveys precisely the same feeling
It's not a perfect translation, as you can "miss a call", "miss a good opportunity", etc and it doesn't mean that you are feeling saudade of it. But this case would be almost ok, just like we don't have a single word, for example, for the verb "to handle", which is a word that has almost the same idea in several contexts but we need a different word for each one ("lidar", "manipular", "mexer", "operar", "cuidar", "tratar", ...)
However, "to miss" is a verb and would be a translation for "sentir saudade". There's still no precise word for the noun "saudade", the feeling itself. Perhaps the closest one is "nostalgia", but it's still not exactly the same as nostalgia has this sense of something that happened in a distant past, and it is more related to the past itself than a person, a thing, etc. Even in Portuguese we have the word "nostalgia", but no one says "estou sentido nostalgia de você", we say "estou sentindo saudade de você". And we can feel saudade of something that happened yesterday, but not nostalgia.
How often do you use the standalone noun out of context though?
Every real world usage of the term I can think of has it in the verbal form: "sentir saudade", "estar com saudade", "dar saudade", "a saudade é grande". Even in the sentence "Saudade" the verb is implied.
In all those cases it can be accurately translated as "to miss".
> How often do you use the standalone noun out of context though?
The same frequency as any other noun of feeling, like happiness, sadness, hate, etc. Saying "to miss" may imply that one is feeling that emotion but doesn't have a name to it, like having the emotion but not having the word that describes it.
Even though there are some ways to describe that idea it needs an extra effort, so it's not well defined as in Portuguese. Imagine not having a word for "responsibility", "power", "partnership" or other abstract concept: you can define them through subordinate clauses but it will not define that concepts (that's why have words).
And just for fun: if Inside Out was made in Brazil I can see clearly that Saudade would be a character (and a major one, the saudade of home is what leads to the climax), but it can't exist because it wouldn't have a word for that. In the second movie we have Nostalgia, but it's a minor character which wouldn't do what happened in the first movie (thus, we can see the difference)
