If you want to make sure the interest rate your lender offers you is the rate you get when you close the loan, ask about a mortgage lock-in (also called a rate lock or rate commitment). Any lock-in promise should be in writing. Make sure your lender explains any costs or obligations before you sign.
It's better to follow the 2% Rule which suggests that you can enjoy the benefits of a home refinance if your mortgage refinance rate is 2% lower than that on your current loan. The interest savings will help you recoup the costs you've paid for the new loan provided you stay in the property for a certain period of time (break-even period). However, there are no-cost as well as low-cost refinance loans wherein the costs are included into the loan. But you can expect comparatively higher rates on such loans. Moreover, these loans are limited when the market is in a credit crunch.
Don't rely on published rates. "No one's going to advertise their worst product," says Keith T. Gumbinger of HSH Associates, a Butler, NJ, firm that tracks mortgage rates. "They advertise the best possible rate, which probably gets offered to only the top 10 percent of applicants."
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.