What does it take for an online-ordained minister to perform a legally binding marriage?

The sea captain thing is mostly a myth.

As long as the state recognizes the ordination, all the officiant has to do is sign the marriage license and file it with the county clerk’s office. The clerk may also require proof of the ordination. But just because that’s all the officiant has to do doesn’t mean that’s all that’s required overall. A lot of states require one or two witnesses to sign the marriage license, and sometimes there are other things the bride and groom have to do (like get a blood test to prove they aren’t cousins). In general, the best course of action is to call the county clerk’s office, get a full list of requirements, and then let everyone who has to do something know what their responsibilities are.

You need to look at your local law (state law in the US).

I looked up our Illinois statute. Basically a denomination can spell out its own rules. And pretty much anybody can say, “we are a denomination”, so a mail-order minister is good to go.

The text of the law:
A marriage may be solemnized accordance with the prescriptions of any religious denomination</strong>...

I’m ordained through the ULC (Universal Life Church) https://www.themonastery.org/

They don’t require you to have any particular belief or any belief at all, and it’s free… so it worked for me.

Rules vary by state. In Florida, where I live, basically if you say you’re a minister you are one. New York and a few other states require paperwork.

I am a Cumberland Presbyterian minister, which is pretty much like the PC-USA (Presbyterians) and United Methodists in their beliefs—a very ecumenical group.

As others have stated, all you need is a “minister” and two witnesses to sign the marriage license. The credentials of the minister are almost irrelevant, as the marriage is pretty much ratified by signing the document and filing it at the court house. In other words, the filing of the license is all that makes you married.