Refinancing a second mortgage tends to be more difficult than a regular refinance. This is primarily because a second mortgage carries more risk for the lender - if for any reason the house is sold or foreclosed, the second lender only gets what’s left over after paying off the first mortgage. As a result, the market for second mortgage lenders is smaller than for first mortgages, and offers fewer options.
But if your credit is good, your income is stable, and your payments have been consistent, you should be able to find refinance options for a second mortgage. As with any mortgage, make sure to shop around to compare interest rates. You should also talk to your current lender, who may be able to offer you refinancing options. This will allow you to save on fees and certain closing costs that are incurred with a refinance. Your current lender may not offer you the best rate, however, so make sure to compare your options!
If the interest rates on your first mortgage are also significantly higher than current rates, it might be in your interest to refinance your first and second mortgage into one lump payment. If you own a significant portion of the equity in your home, you might also consider using a line of credit (HELOC) with a low interest rate to pay off the second mortgage, rather than refinancing.