Nebbie actually has a bit of white. Couple spots on her lower chest and belly. Then a white smudge on her hip (you can kind of see it in the picture). That is how she got her name... all black, like outter space, with that little random 'cloud'. Her name was Lily when I adopted her, but she doesn't seem like a Lilly to me (not white, and certainly not lady-like/dainty!)
Another thing you could do, is post a "FOUND" ad in local lost and found resources. Be careful however, as lots of people will take advantage and try to get a free cat. If she will let you hold her, try to look for ANY kind of markings...usually black cats will have some white, even if it's just a few hairs on their neck, or something. Or if her eyes are a certain color (even just "yellow" has traits like bright yellow as to darker gold). Just don't put these details in the ad, only say "black cat, call for identification" and let the people tell you what the features are... if they get them right, they are most likely the true owners.
I don't know a good time to wait... probably no more than 6 months?
The last cat I "found" ended up being my ex-husband's! He lives in North Dakota now. Earlier this summer a tortie came to the door and was begging to be let in! So I knew she was a pet, and let her in. It was a Sunday, so all shelters were closed. That night I posted ads in the local classifieds (also asking for details, as her paws have a certain pattern), and called all the neighbors (of course the ones that didn't answer ended up being the one I needed!). In the morning I loaded her up to go take her to the rescue group I work with to see if there's a microchip. Then I noticed my ex's car in his parent's driveway - they live across the street and down 2 houses. This cat seemed like just the kind he would have, as he likes Torties... so I figured I'd take the chance and ask. Sure enough, it was his. His parents were supposed to take care of her while he's away, but she came over to my house since she recognized it as "home". I dropped her off... but the next day she was back again. I agreed to take care of her, as I didn't want her to keep crossing the street and risk getting hit by a car. I have to keep her outside, as I'm really not allowed to have any more cats. (and now it turns out that my husband's place won't allow cats either...so I guess I'm stuck with her!)