You can also save money on your mortgage refinancing by paying "points." This is a fee that effectively lowers the interest rate of your loan. If you plan on staying in your home for a long time, this long-term strategy can be an excellent way to save thousands of dollars.
Ask for more than just rates. Bad loan officers will tell you anything to keep you on the phone -- then change the details to suit them later. Instead, make them get real with you! Ask how long they've been in the industry. Probe them about their experience in the industry. Also, ask what their opinion is on the current market and where it's going.
You have a legal right to a good faith estimate. Get a copy of this document and go over it with a fine tooth comb, it will reveal where there is a real problem.
Pull your credit report from the bureaus and review it for any negative items (late pays, collections etc) and inaccurate detail. Try to dispute negative items and remove them from the report. If required pay off any unpaid debt. Otherwise, you won't get a low rate and may not even qualify. Of course there are lenders in the subprime market who may offer you a bad credit refinance loan, but it's better to avoid them as they'll possible charge higher rates and fees.
If you plan on moving out of your existing home within the next few years, it may not be beneficial for you to refinance. Make sure you let your mortgage specialist know your future plans.