In code, you have the ability to make a phone number on a website into a link by prepending the phone number in the href with a "tel:"

So, for example, you can create a link to 800-867-5309 with the following:

<a href="tel:+18008675309">800-867-5309</a>

Some phones will automatically turn any properly formatted phone number into a link that, when clicked, will prompt you to see if you'd like to dial said number (iPhones for example).

Does it make sense to do add these links manually so the phone numbers show up linked on desktops?

On a desktop computer, when you click on one of these links, the computer will try to open some sort of default communication program.

If you have not set a default communication program, this might be a little jarring as it might open a completely unfamiliar program, which I would think falls under the "unexpected results" realm.

Is there any best practice for this sort of thing?

Should phone number links, perhaps, be formatted differently than other links?