The recent reduction in interest rates by the Federal Reserve doesn't necessarily result in a lower rate for fixed-rate mortgages. This is because bond rates, not the fed rate, drive fixed mortgage rates.
And, you've probably heard that it only makes sense to refinance your mortgage if the new interest rate is at least two percentage points lower than your current rate. Well, forget that advice. It may have worked in the days when you could only get a 30-year fixed rate mortgage. It doesn't apply in today's financial markets where there are many options for financing your home, including fixed mortgages with terms of 15, 20, or 30 years; five- and seven-year balloon loans; and a wide variety of Adjustable Rate Mortgages (ARMs).
Even if you can't lower your monthly payment by refinancing, it might make sense if you can give up the insecurity of an ARM for a fixed rate.