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 is feasible to go for a refinance when you have built up at least 10% equity in your home (For Fannie Mae owned mortgages, the value is 5%). It is also possible for you to choose the option if your equity is less than 5%, but you may have to pay a certain amount of cash in order to make up for the difference in equity.
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.
If you are paying private insurance on your current mortgage, refinancing may allow you to do away with this unnecessary expense.