Strangely the hardest part seems to be figuring out which story goes where. Not that any of it is easy
I looked up 4 popular authors who contribute a lot of series short stories to anthologies on fantastic fiction, Wikipedia and their own web sites.
Only one had a list of short stories and the series number info was not there.
So in order to do this you have to determine which stories are part of a series, and where they fit. Not hard with one anthology but if you are talking say 50 with 10-20 stories each, too daunting for me.
calibre is unlikely to do this as it would mean parsing each book's TOC assuming there is one, and downloading metadata for each story.
As unboggling said, you could add an empty book for each story you care about, fill in the name and author and 2 times out of 3 calibre will download the series info for you. Often the metadata download will even put the anthology name in the comments field, and download a cover.
Me, I just read the anthologies when I read them as the short stories are pretty much stand alone and rarely contain spoilers.
Helen