Saudade is a Portuguese word that is famous for being difficult to translate . It refers to a longing that negates the present time for enjoyably missing a pleasant memory in the past or a pleasant possibility in the future, although with a conviction that it’s really impossible because it’s lost or perhaps never existed.
I think saudade is “melancholic desire” . It’s remarkable that the concept implicitly contains the possibility of mourning  in the last part of the definition above (“perhaps never existed”) which adds a crucial ambiguity to saudade that is essential for the concept’s perceived profundity.
Insofar as saudade is attached to a past memory or a future possibility, it still refers to an actualization in time, and it’s still a simple negation of the present time. It’s a staged loss, a melancholy, and it’s unaware of the staged status of its loss. On the other hand, when you add the proviso “perhaps never existed”, the saudade can be detached from actualization and can move to another virtual dimension where the past is linked to the future through the present time’s negation of negation. In this case, the staged status of the loss can be revealed, and the loss can be properly mourned.
Thus in saudade, there is (1) a profound attachment to the emotion of longing, and also (2) a deep suspicion that the longing is illusory and false. The second aspect is sometimes repressed by the first aspect, e.g. in efforts to define saudade as “a truly authentic longing that’s specific to Portuguese people”. Of course the Portuguese people deserve to claim the universal value of their concept, but only with the crucial proviso “perhaps never existed” that leaves the saudade in a fragile balance: Saudade means that your deep longing for X captured by the name “X” perhaps has nothing to do with X. With this unconscious knowledge of dissociation, saudade triggers a separation of words from things, or a separation of the symbolic from the real .
It’s remarkable that the saudade is more and more profoundly felt as the suspicion that underpins it becomes stronger and stronger. This dialectic is akin to the phallus as the signifier of symbolic castration. Saudade is divided between (1) a perverse drive to yoke the object of saudade (objet a, “it”) to a phallic Other (such as the “Portuguese nation”) and (2) a hysterical desire to question and undermine such efforts to instrumentalize “it” by declaring the independence of “it”.
This gives us two ways to “kill saudade” (a Portuguese phrase): either (1) the presence of a phallus (something or someone) emerges and expels the longing for “it”, desire is “fulfilled” or “satisfied” or rather covered, saturated, smothered, repressed before returning again later, or (2) the subject reconciles himself/herself with the virtual dimension of “perhaps never existed”. This second way is proper to mourning and separation .
 See Wikipedia and Brittanica on saudade. Some Portuguese people point to the current common use of saudade and say that it’s just “missing” in noun form, whereas other Portuguese people agree with me and understand my message here. I think their disagreement is inherent to the concept itself and proves the universal value of saudade.