There is a category of shoddy promotional item known as the carabiner mug. It's the kind of freebie you eagerly grab at a trade show because it seems nifty, and when you get home you wonder why you bothered; they're tiny and usually hold just 7 or 10 ounces, and the poorly-mounted carabiners are often of poor quality themselves.
However, if this object appeals to you, REI makes a more robust, double-walled stainless steel line of these. The basic version holds a proper 16 ounces and comes with a lid.
The travel version also holds 16 ounces, but is shaped to fit into a car's cupholder.
They also make a 14-ounce version with a screw-on lid, if you're looking for a more secure seal.
The handle on the last one is rather interesting: I thought it was a spring-loaded carabiner-style action, as on the first two, but instead it's this:
I don't think I've ever seen that before. I wonder what the green part is made of, but the product page doesn't say.
One issue with all of these REI mugs: Supply chain issues are real. All three of them are currently out-of-stock.