I dont know enough about smart watches but i figure that at some point, browsing web sites on them will become a standard feature. The "Web Browser for Android Wear" app on google play has more than 100,000 downloads and the "WebBrowser for SmartWatch" app has more than 10,000
To that end, given that smart watches like Sony's SmartWatch 3 has a 1.6” screen, what should web designers need to take into consideration when making their web pages as portable as possible? Is there a set of standards? What kind of functionality and behaviour should one expect of a page displayed in a smart watch browser?
Although SO isn't the best place for this question, I'll chip in. As far as I know, designing for wearables is still a new thing, and as per say, I haven't come across any standards as such.
But I think responsive web design should do just fine. People are working on designing websites for smart watches. Here.
However, think about using the standard manufacturer APIs to build more robust and interactive experiences than just relying on websites on tiny screens.
Here's an article from Net Tuts+ that shows you how to design for the Apple Watch using existing web technologies. Bear in mind it doesn't beat native at all.