Do not rely on any estimates over the telephone, they're worth the paper they're written on. Compare the lender's fees only. A lender can deliberately underestimate outside service costs to make the total loan costs appear to be a bargain. Make it clear to the lender that you know that they cannot charge fees later that were not reasonably estimated upfront, it's illegal. Find out if the rate quoted can be locked for the period of time you need to close the transaction.
Lenders often give use the shortest lock period, one or two weeks, to give estimates.
For purchases, a lock should be for a week or two past the scheduled closing date. For refinance, you should have at least 45 days. You always should have more than is necessary to allow for unforeseen delays. Bad lenders may deliberately delay to go past the lock period and force a higher rate.