I had the opportunity to use the internet on board the Radiance and it worked fine. Like Queen of Diamonds I like to check briefly my email to be sure family and friends are o.k I noticed it was working very well for everyone else who tried too.
No it wasn't as fast as my home internet but it wasn't agonizingly slow either. I did make a mistake at first...I tried to log on using my local home server which BTW is lousy even on my home turf...finally after noting everyone else's success I got smart and used one of the featured servers on the screen. Perfection....
Now for just web browsing it might not be that great.
My husband and I have iPhones and kept them in air plane mode where we could listen to music etc. but we couldn't check our email or send text messages. The cost would have been outrageous because we would be charged by the minute as the phone attempted to down load all email, text messages and updated apps, and iPhones WILL try to update and download automatically when you first turn them on. And at sea this would have been super slow and $$$$$$$