calling within Switzerland while using U.S. carrier

The way you should do it is store all your numbers in your phone in the standard international notation.

That is +(country) (area) (subscriber)

So for Switzerland that will eg be +41 11 222 3333
For a US number this is for exampl eg +1 123 56 78 90
And so one.

If you do that, then your phone will just automatically do the right thing no matter where in the world you are.

WengenK nailed it. That is the format of all my phone numbers in my phone, and I put in numbers for hotels in Europe, etc., before leaving home.

OP: Verizon has an info sheet they emailed me when I recently signed up for their monthly plan that explains what you need to know for placing calls abroad, including any numbers to connect with Verizon in the countries I am visiting. Surely ATT has a similar info sheet on their site?

I have Verizon, but when I made calls in Switzerland back to the US, I just clicked on the name in my contact list like I do back home. My phone knew what to do and connected the call. I didn’t have to do anything differently.

I just looked and the numbers in my contact list are just area code and number. I did not need to add a +1 when I called from Switzerland. These smart phones are very smart. 😊

Our cell phones are using an AT&T plan, presumably based in the U.S., with roaming privileges

Your AT&T plan is definitely, not presumably, a US based plan. I am sure that like my carrier Verizon, AT&T has an international roaming plan that you have to enroll in (you don't just show up in Switzerland and assume your phone will work) that allows you to use your phone abroad, but what actually happens is when you turn your phone on abroad, you are paired with a cellular network in that country, technically you are no longer using your AT&T cellular service to make and receive calls, texts, etc.

Just clarifying since you sounded a little unsure of how this works, and to make sure you signed up for the plan, too.

Here is the info. for ATT specifically on making international calls:

https://www.att.com/support/article/wireless/KM1009432/

But Verizon has similar instructions and like I said above, I don’t need to add anything to the contacts in my list.

And adding to what jojo stated, I do sign up for verizon’s international plan before leaving the US. That way, my phone works as it does in the US.

Here is info. on the international plan options from ATT:

https://www.att.com/international/