It's hard to say goodbye to old friends, so here's a thought: don't do that. Instead of leaving them behind, bring them with you. Even when you start playing a different game.
The New Vegas Companions mod transplants some of your favorite companions (though maybe not your most favorite companion) from Nevada into Fallout 4. And you don't even need to pick them up at the airport, though you will need to venture into another Fallout 4 mod, Project Mojave, to reach them.
Project Mojave, as you might know, is a mod that adds locations from Fallout: New Vegas as playable areas in Fallout 4. It includes the Vegas strip, Nipton, the Good Luck Trailer Park, several casino suites, and more. And if you visit those areas with the New Vegas Companions mod installed, you'll be able to find and re-recruit some of your old friends.
The New Vegas Companions mod includes gutsy caravan owner Rose of Sharon Cassidy, gunslinging ghoul mechanic Raul Tejada, Brotherhood of Steel scribe Veronica Santangelo, and reformed Enclave member Arcade Gannon. Each has full introductions when you meet them, they can be brought to settlements to live and work like your regular Fallout 4 companions, and they have combat and follower dialogue, too. You'll find Arcade and Rose at the Mojave Outpost, Raul at the Nevada Highway Patrol Station, and Veronica at the Mojave Drive-In.
Note that their dialogue files are a separate download from the mod files on Nexus. Here, take a look at your old friends in action in Fallout 4 and grab the dialogue files in the video's description:
I'm guessing a good percentage of people reading this are saying: Yeah, but Boone. Where is my Boone at? Well, there's good news and bad news. Boone is indeed included in the mod. You can find him in one of the homes in Nipton (hopefully it's an upgrade from living inside a giant plaster dinosaur). But according to the mod's page, "Boone is not included as a follower due to difficulties making his dialogue work." So, you can go visit your favorite brooding sniper, but you can't take him with you on your adventures. Alas.
You'll find the New Vegas Companions mod here at Nexus Mods.