Know your credit score before you begin looking for a loan. If you can, try to remove any blemishes from your credit report before applying for a refinance.
Close inactive credit card accounts to improve your credit score, making you eligible for lower interest rate loans. You will need to notify the credit card companies in writing that you wish the accounts closed on your request. Next, check your credit report after 30 days to be sure closed accounts include the comment "Closed at Customer's Request." You want future lenders to know it was your request and not bad credit that closed your accounts. Also, take the time to check for any mistakes in your credit report that could negatively impact your credit score.
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.
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.