If the bonds have stopped earning interest it probably makes sense to cash them in. Unless an election was made to tax the interest earned on an annual basis all the interest on EE bonds is taxed when you cash in the bonds. Most people choose to defer or delay paying income tax on the interest earned by their savings bonds. You will need to determine what happened with the bonds you inherited.
Since you have stated the bonds are no longer earning interest it implies they are 30+ years old. Because the bonds were inherited there may be several issues to deal with depending on the size of the estate, how the bonds were titled and where they were held. A detailed discussion is beyond the scope of this forum. If you are dealing with significant dollar amounts seek the advice of a competent estate and tax attorney and or CPA. Or provide some more detailed information and I may be able to provide some more feedback.
A few resources from Treasury Direct that might help:
Series EE Bonds
Tax information for EE and I bonds
Death of a savings bond owner
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