I just refinanced, made my first "new" payment on a 15 year refinance at 2.25%. I wish I shopped around more, but in the end it turned out well. I got immediate calls from Quicken and started the process w/them, they were very good to start, got me a 2.99% rate on a 15 year w/limited fees, then someone from Loandepot called mid-way through and said their goal is to always beat Quicken b/c they are #2 to them, and they will ALWAYS beat them. So I gave the benefit of the doubt and right away they gave 2.75% and lower fees, so I switched over and Quicken stopped returning my calls. So I just phased out w/them and continued w/Loandepot. I paid some points to lower it to 2.25% (lowest rate) just b/c we plan on being here for 15+ years, so over the lifespan it saves a decent amount of coin as long as I don't pay it off too early (since fees would exceed at that point). So we're just changing our strategy from before (prepaying more money to principal) to standard payment and then invest the rest.
On that note though, we were able to get such a good rate and an easy process b/c we paid down our mortgage a decent amount over the last 6 years. Long story short, shop around, even if you go w/one of the "big guys" they can sell your loan (ours already got sold to Mr. Cooper or something like that), so it can get sold no matter who you go with, so work on them to get the best rate, make them compete against each other, even if you've started the process w/someone else. As long as you haven't signed the final paperwork you are still fair game.