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)
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".