My partner brought her cats from the USA (near Boston) to the UK. BA were good, and very careful.

Make very sure the container meets airline specifications, has food/water dispensers to use, and is big enough!! Attach some dry food in a bag on the outside, and label the box with the pet name and your contact details.

One of her cats was very fluffy and appeared large. BA would not accept it and she had to source a larger animal carrier at no notice, as well as find overnight accommodation for herself and two cats. So err on the size of large for the carriers. If you've got any sort of Maine Coon or more muscular cat, get an oversize (dog) carrier for the cat.

It's not cheap. It'll cost more to transport the cats than it will a person in economy (on a return ticket, even if the return is discarded).

Make sure the paperwork is up to date and in particular make sure that all the documents have the correct, same, microchip number (and that the microchip is the sort readable by European chip scanners). Otherwise you're in a world of trouble (and since the documents can be handwritten, transcription errors are possible). Avoid sedation, the animal has to look like it's not sick or otherwise unable to travel.

Don't use United. Their animal cargo death rate is much higher than anyone else's (only partly because they carry higher risk animals). Avoid any airport transfers too.