Be Patient. Processing all of the paperwork that's required for a new loan takes time. Be patient while your loan moves through the system. Protect your credit score by paying your bills and making your mortgage payments on time and not taking on any more new debt than you absolutely have to.
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 your new mortgage rate seems too good to be true then it probably is. Check for hidden fees in your mortgage that will make up that suspicious difference.
Ask the company carrying your current title insurance policy what it would cost to reissue the policy for a new loan. This may reduce your cost.