This can resolved by transferring the membership to a "Dummy" (duplicate) constituent record and merging the source record back into the target record (if this is a scenario where there are two duplicate records with duplicate memberships, begin at step 6 below and use the actual duplicate constituent instead of the "Dummy").

NOTE: This process will not work if the Membership status of one of the Membership records is "Cancelled." Follow the steps here to view the member's transactions, and highlight the "Drop" and click "Delete." This process will also not work if the Membership program allows multiple memberships. You can edit this setting in your membership program to merge memberships by going to your membership program and clicking Edit on the General Tab. Here you can uncheck the box "Allow multiple memberships." 
  1. Go to Constituents > Add an individual Add a new Constituent with only a last name as this is the only required field (this will be the dummy record)
  2. Go to the Membership page of the Constituent with the duplicate memberships
  3. Go into the Membership that is current
  4. Click Other Tasks > Transfer Membership
  5. Select the dummy record and transfer the membership
  6. Go to Constituents > Duplicates > Merge two constituents
  7. In the Source constituent field, select the dummy record
  8. In the Target constituent field, select the normal record
  9. In the Merge Configuration drop-down, select Default Configuration
  10. Select to "Delete source constituent"
  11. Click Merge