The best replacement for jurat is affidavit.

The best alternatives to jurat are rated as following:
★★★★★  affidavit
★★★★  acknowledgement
★★★  acknowledgment
★  acknowledgment notary

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Speaking about jurat, one probably shouldn't forget about affidavit.

Other search terms related to jurat and their ratings are:
★★★★★ affidavit
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