We have used http://www.romeinlimo.com/ a couple of times for transfers from the Civitavecchia cruise port to our hotels in Rome and a couple of private tours while there. We thought their transfer prices were reasonable, 140 Euro for 4 pax in a Mercedes van port-hotels (but as compared to the nearly $700+ the cruise line wanted to charge for the same transfer, anything is reasonable ).

On a cruise last year we had them give us a quote for a day trip around the Amalfi Coast as I wanted my husband to experience the drive to Ravello & visit more towns along the way, but in the end we decided to visit Capri for the day instead. I mention that just to say they are willing & able to arrange transfers to/from that area if you want to get a quote by means of comparison, they don't just work the Rome area (i.e. compare transfer from FCO vs. from Naples train station in terms of price, time, hassle, etc.).

On an earlier visit with my brother we took the local train (mentioned above) from Naples to Sorrento. But if you're on your honeymoon I would recommend a car service as that train reminded me of riding the T in Boston and you probably want a more luxurious experience on your honeymoon. (Don't get me started on my husband's great idea to take a coach from DUB into the city for a 'short walk' to our hotel on our honeymoon...in the rain! All was quickly forgiven when we got to the hotel & learned they had upgraded us to a suite, but still. ).