TOEFL iBT: To appeal your TOEFL iBT score, you can request a formal review for the Speaking and/or Writing sections through your online ETS account. The Reading and Listening sections are computer-graded and not eligible for review. It is crucial that you submit this request within 30 days of your test date and only if you have not yet sent your scores to any institutions. This score review service is not free and requires a fee; however, the payment will be fully refunded if the review results in any change to your score. The process typically takes one to three weeks, after which the new score—whether it has increased, decreased, or remained the same—becomes your final, official result. 
For more information: http://ets.org/toefl/test-takers/ibt/faq/score-reports.html

PTE Academic: To appeal your PTE Academic score, you can request a rescore for the spoken and open-ended written sections by calling Pearson customer service within 14 days of your test. This service is only available if you have not yet sent your scores to any institution or booked a new test, and it requires a fee which is only refunded if your overall score changes. A score change is unlikely as most of the test is machine-graded, but be aware that the new score—whether it is higher, lower, or the same—will permanently replace your original result. 
For more information: https://www.pearsonpte.com/policy-center/rescore-policy