Alas, there isn't really
Based on some further research, it looks like a better shield UI has been a community and developer "wishlist" item for years, but doesn't seem to have been implemented.
One of Blizzard's community managers explained it this way in 2014:
Oh, I've actually wanted to talk about this for a while and hadn't found a good opportunity. :)
We really like the idea of having a shield indicator on the UI (myself included, and you can bet I gave some sad puppy dog eyes when I noticed it was removed as I'm over-paranoid about dying and generally run a lot of shielding abilities). However, the version we had on the PTR/Beta wasn't really fulfilling our needs, primarily because of health scaling.
To clarify, there were cases where, because the amount of shield provided could be so small in relation to your overall health pool, the shield graphic was hard to see. The first iteration, where the shield graphic completely covered your health globe, was less than ideal because you couldn't tell how much health you had remaining under your shields. The small curved bar on the right side of the globe was better, but scaling issues persisted.
In short, it's a UI update we want to revisit in the future, but it wasn't up to our quality standards. When it comes time, we want to make sure what results is smooth, easy to read, and makes sense.
Since then, there doesn't seem to have been much movement on this.
Unless the UI changes, about the best you can do is to get better at guessing how much shield you have left using practice and experimentation.
For the sake of completeness, note that the current UI provides these (limited) features:
Holding the mouse over your health globe will show your current shield value (a single sum, even if you have shielding from multiple sources), as seen here:
Aside from the popup, there is no visual indication of how much shield you have on the health globe.
When the word "Absorbed!" appears over your character's head, you are taking shield damage.