Hi -
My initial reaction is that it's one of those old Swiss companies, but then again, Google is your friend. There *was* apparently a Sentinel Watch Company in the US, but I don't have any information beyond this
link.
What put me off right off the bat is that the lettering doesn't look, well, refined, and it's opticallly a mess: the word "Sentinel" on the face seems to grow smaller from left to right, and neither "SHOCK-PROOF" nor "INCABLOC" are centered, which initially led me to think of someone having perhaps labelled it themselves (I've come across some very poor pocketwatches that some enterprising watchmaker put his own label on dating back to the 1920s or so, where the labelling effort really detracts from what otherwise might have been a fairly nice vintage piece.
My guess - and it really isn't anything more than that - is that there was a Sentinel Watch Company in the US from, say, the 1920s through the 1950s, but not later than around 1970. From the watch design, I'd put the design from the end of the 1950s to the early 1960s, almost definitely a Swiss watch made for US consumption. To be quite honest, the face design reminds me of a Pierce from the same time period. A lot, as a matter of fact, but that may be more the hand design - baton with pointer extension that are exquisitely designed: the minute hand goes to just short of the minutes, and the hours hand covers roughly 1/3rd of the hours numerals, giving the face a really nice design that wouldn't have been found in something quick-and-dirty done by a watchmaker seeking to make a quick buck.
Any chance of seeing the calibre inside? If you don't know how to open it, the please don't: but do get it to a watchmaker to have it cleaned and oiled and otherwise taken care of. The worst thing that can happen to a vintage watch is to have it completely neglected for many, many years and then have it used without being properly cleaned and oiled. Given that this was you grandfather's watch, it should have significant sentimental value for you. So get it to a good watchmaker and let us know what he/she says about the calibre inside. That could really help in identifying what the pedigree might be. You'd be surprised sometimes what's inside some of these watches!
Enjoy that watch! Certainly unique, even if not easily identifiable...
JohnF