The best replacement for standardized testing is authentic assessment.

The best alternatives to standardized testing are rated as following:
★★★★★  authentic assessment
★★  assessment
★  non standardized testing
★  alternative testing
★  portfolios
  alternative assessment
  criterion testing
  non-standardized testing

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Speaking about standardized testing, one probably shouldn't forget about test anxiety.

Other search terms related to standardized testing and their ratings are:
★★★★★ test anxiety
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standardized testing
authentic assessment
assessment