How to carry phones as presents to the USA from Europe?

Your best bet is going to depend on size. If you can, Carry on (hand luggage) is usually safer. Luggage handlers don't always take the most care with the luggage.

DCTLib has it right but there is a bit more to add.

I will say stuff in this answer that is not 100% factually correct, but the point is to have you have an easy time. Note that the workers doing the inspection and collection won't have all the right info either, so it's better to just go with "common knowledge" then try to pass on an edge case.

Once at your destination you will have to declare any items that are going to stay in the U.S. Gifts and the like should be in their original boxes if you can, and you should have receipts if you can. This is important, not because of rules, but because it just makes things easier.

If things have receipts then there is no doubt about the value declared. This is especially true for items that have a much higher price here than there.

If things are in original boxes, then, again, you have less confusion about what a product is. Especially true for odd or interesting products.

Don't try to bring food of any kind. It's just a hassle.

With electronics be very aware that they may be illegal in the US or may not function on the same frequencies in the US. Thinks like DVD players and game consoles are still region locked (as are the media you use to play on them), and all electronic devices that send or receive any kind of a signal in the US have to have that FCC statement. Customs won't care about that (or at least I have never seen them care), and I don't know of any task force running around checking for FCC statements on things, but it would suck to bring over a new X-Box only to find out it won't work here.

Don't wrap or seal any of the presents. Be prepared to have to open and display them.

Finally, stay away from anything odd, or unknown in the US or be prepared to explain/demo it. Again original boxes help with this. This means having phones ready to turn on, laptops in a state where they can be powered on, etc. etc. It's not really customs job to even look at these things unless they suspect some kind of fraud or smuggling, but... While you would win, after a fashion, a dispute with an agent about not having to turn on that odd-looking camera, and how they really even shouldn't be looking at it, just maybe checking off that it's on the form. It's usually faster to just power it up and let them see.

As a bonus, when filling out the forms be as open as you can be. For example "Digital Camera" instead of "Canon PowerShot ELPH 180 20.0 MP Compact Digital Camera - 720p - Red". If you get an overzealous agent, and they see "Canon PowerShot ELPH 180 20.0 MP Compact Digital Camera - 720p - Red" They could actually try to see the part numbers and sizes and such, but "digital camera" there's not a lot to check.

For example:

Declaring 10 items in a brown cardboard box means pulling out each item and matching it to the description on the form.

Declaring 10 items in the original packaging means just looking at the boxes, except that one marked "Digital Camera $50" that is in a 4' x 4' x 4' box. They may ask you to open that one.

The best solution is to indeed put them into the hand luggage and then watch them closely during the flight. This reduces the risk of them being stolen in transit - at least if you are not sleeping on the flight, that is. It is allowed to transport them in the checked luggage, though.

As far as customs is concerned, it does not really matter. When entering the US, you will have to declare everything that stays in the US (see https://help.cbp.gov/app/answers/detail/a_id/975/kw/Duty%20Free%20allowances%20for%20visitors if you are not a US resident), and you will do so at the airport at which the flight to the US lands. Unless the phones are quite cheap, you will have to pay customs. Presents also have to be declared, so this makes no difference here. Don't gift-wrap the phones in Denmark so that the customs officer can have a look.