From the Wikipedia entry for the Galician-Portuguese word “Saudade”, which I discovered through the twitter feed of Anuskha Jasraj (@anushkajasraj):

Saudade was once described as “the love that remains” after someone is gone. Saudade is the recollection of feelings, experiences, places or events that once brought excitement, pleasure, well-being, which now triggers the senses and makes one live again. It can be described as an emptiness, like someone (e.g., one’s children, parents, sibling, grandparents, friends, pets) or something (e.g., places, things one used to do in childhood, or other activities performed in the past) should be there in a particular moment is missing, and the individual feels this absence. In Portuguese, ‘tenho saudades tuas’, translates as ‘I have saudades of you’ meaning ‘I miss you’, but carries a much stronger tone. In fact, one can have ‘saudades’ of someone whom one is with, but have some feeling of loss towards the past or the future.

By the way, Jasraj is the author of the gem “Radio Story,” which won the 2012 Commonwealth Short Story Prize for India. You can find it here, on Granta’s New Writing page:  http://www.granta.com/New-Writing/Radio-Story