Could it be a salt cellar, minus the glass liner?

The fish is a silverplate mark - Hans Jensen

http://www.925-1000.com/silverplate_J.html

Thanks! Jensen: interesting. My Danish grandmother was a Jensen. Looks like Eisenberg-Lozano mentioned corresponds to that logo under the crown, too. :) The E looked pretty clear but the second letter I was not sure about.

Found this on ebay:

http://www.ebay.com/itm/291526678961?rmvSB=true

It’s much too small for either pickles or jam. Unless you wanted
a container to hold maybe 2 whole small sweet pickles… on their sides. ;) It’s about the size of my
thumb width and lengthwise. Actually depth is about the size of my thumb, too. Scale
was part of the reason I didn’t crop my fingers out of the photos.

I have a hard time seeing this for salt, either. It would be
awkward to scoop it out when it ran low. I imagine all the times this would get
knocked over on the dining room table.

Bet it's a cigarette holder.....
back in the days when every one smoked, it was a custom to have ashtrays on the dining table and several holders for a few cigarettes.

https://www.etsy.com/listing/473232066/coalport-june-time-cigarette-holder-and?ga_order=most_relevant&ga_search_type=all&ga_view_type=gallery&ga_search_query=cigarette%20holder&ref=sr_gallery_34

Wow! That could be it! Shape would be just right. Now to figure out what I'LL do with it.

Thanks. What about the openings on the sides, though? Its really narrow for scooping salt out, too.

If you and your guests don't smoke, find a glass that will fit inside and use it to hold a tiny bouquet.

Well, salt cellar does seem the most likely. Thanks! Though it's so deep it's hard to imagine that being practical to scoop out.

I have my Danish Grandmother's salt cellars and spoons. But those are just little round cut crystal dishes, the kind that you normally see. I remember my grandparents using them at the table in the 1960's. It was hard to see past that notion to imagine a different shape.

Maybe it was used (with glass insert) to hold mustard ?