Car service from Rome airport to Sorrento

A taxi would be a fortune with a 3.5 hour drive, and then they would need to return. There is a 1 hour train from Rome to Naples, and then from the same station (although a different floor) you can ge a train that will end in Sorrento. I just took it 2 weeks ago and I think it was 4.80 eu each and about 1:15.

Not many of this site would do that so information may be limited. My guess would be in the range of 500 Euro. It is easy and cheap to do it via train but you didn't indicate the amount of luggage. Anything more than a bag or two per person could tip it back to a private limo. You might contact Romecabs.com for a quote. Contrary to the "cabs" in the name, it is actually a private limo company.

To reduce the cost ( I’d guess over 600 euros) you could take the fast train to Naples then have a driver pick you up there

We used this company for transfers in the area

https://www.topexcursionsorrento.com

You could also do a price estimate on Daytrip (used to be Mydaytrip).

https://daytrip.com/landing/rome-to-sorrento?gad_source=1&gbraid=0AAAAADfljqyvn2hBWerve0lBkLfqF5LtU&gclid=EAIaIQobChMItNDZvYi-iQMV2zfUAR1jITGREAAYAyAAEgI-PvD_BwE

I plugged in a random May date and time for a ride from Roma Fiumicino to Sorrento and came up with an estimate of $771 US.
Given the heavy traffic in high season, I'd go with "fast" rail at least as far as Naples. It's nice to be able to get up to stretch, use the facilities as needed and even picnic in your seat without losing any time to stop for any of that. Buy picnic provisions at the train station before boarding.

Whether to go onward from Naples Centrale to Sorrento via Circumvesuviana commuter rail or private driver is up to preference and budget. With 4 of you to split cost, a driver would be a logical choice, IMHO, and be able to drop you off as near to your accommodation's doorstep as possible.

It's hard for me to rate four hours in a car as "luxury" versus 1.5 hours on (two) trains, and 55 minutes in a car service from Naples to Sorrento. I'm proposing the Airport Express train, FCO to Termini Station in Rome, and the Frecciarossa "fast train" to Naples, just over an hour. However, it's hard to buy a changeable Frecciarossa ticket that's as cheap as a non-changeable ticket, in case your plane is later, or you have baggage claim problems. No reservations needed on the Airport Express.

Note that four people and luggage are a tight fit in a sedan, so you may need a premium vehicle, as well as a four-hour empty-return cost. I agree with the 500 Euro estimate/guess, but as a LOWER bound. A black car from the Naples rail station to a Sorrento hotel might be 125 to 150 Euros, but I haven't done it lately. The hot, crowded, gritty Circumvesuviana commuter train (not recommended) is just a few Euros per person, Naples rail station to Sorrento downtown. Might still need a 15-20 Euro cab in Sorrento, depending on hotel, weather, etc.

In 2017 we used topexcursionsorrento.com for our transfer from the airport in Rome to Positano. We were a party of 4 and it was well worth the money to just be driven especially since we were headed to Positano(not being an easy destination to get to from Naples). We were met inside the airport and our driver, Giovanni quickly helped us with the luggage and we were on our way. Lovely to just sit back and enjoy the scenery after a long flight. We stopped for a restroom break and also for pictures while the sun was setting.

I'm thinking we paid 600 Euro's.

It's hard for me to rate four hours in a car as "luxury" versus 1.5
hours on (two) trains, and 55 minutes in a car service from Naples to
Sorrento. I'm proposing the Airport Express train, FCO to Termini
Station in Rome, and the Frecciarossa "fast train" to Naples, just
over an hour.

I agree, a 300 km/h train wins over a car every time. And gives you access to a bathroom as well as an onboard bistro where you can get food, coffee or something else without having to stop.

The hot, crowded, gritty Circumvesuviana commuter train

Note that the Circumvesuviana is getting less hot and less grittier. And maybe less crowded. https://www.railwaygazette.com/traction-and-rolling-stock/circumvesuviana-fleet-modernisation-gets-underway/67616.article

I looked at a Rome airport to Naples private transfer for this month awhile ago for 4 during lower season. The cheapest I found was 450€. I’d add some to that so maybe 550-650€.

That's great news, Badger! :O)
We used it between Pompeii and Sorrento without issue but I know it hasn't been everyone's favorite mode of transport. Heck, for the LOCALS who use it frequently to go about their work and errands, I'm sure a bit more comfort will be welcome.

We used Aldo Limos from Sorrento to Rome airport, took about 3.5 hrs, cost about 500 euros, for two people, May 2023. I would highly recommend this service. You would have three trains to get to Rome airport from Sorrento. Relax and splurge, perhaps? Christine is the Sorrento office is a Brit, so email communication was easy.
Also- book the Rome airport hotels early, as they fill up quickly, and the price increases. There is a regular Hilton and a Hilton Garden Inn.
Have a wonderful time!

We priced this out for our trip in Spring 2023 and the cost was a bit over €600 for two people. Option 2 we looked at was taking the train to Naples and then a car from there at a cost of about €150. We ended up taking the train to Naples and then catching the local Cicumvesuviana commuter train to Sorrento. We then caught a cab to our hotel which ended up being about a 10 minute walk away for €24 (taxis in Sorrento and the Amalfi Coast will not be cheap). In hindsight, after an overnight flight I wouldn't recommend the way I did it. But we also weren't willing to pay the high prices of a taxi or driver. If we ever do it again we'll spend our first night in Rome and get a fresh start in the morning by train.

Allan’s got great advice about taking the trains.
Taxis where I live ( San Diego) are quite expensive when you figure what the cost-per-mile is.
The taxi fares in Italy are probably double what they are here and they are stunningly expensive.
A shuttle service may be slightly less expensive.
European trains and buses are the way to go.
For the best prices on Trenitalia high-speed trains, buy your train tickets 90-120 days in advance of the train’s departure date. For Italo trains, tickets go on sale 6 months in advance.

I would not refer to the taxi fees in Rome as being "stunningly expensive." We have used Rome taxis for years and thought the fees were reasonable. Even Steves agrees in some of his DVDs. We frequently use taxis in Rome. Rome taxis can only be engaged at a taxi stand and if you order a taxi the meter starts when the taxi gets the call. Too practices not common in the US.

We’ve never paid more than 10-12 euros for a taxi ride in Rome
( other than the flat rate from airport now 55 euros )

That is not “stunningly expensive “