The best replacement for bearnaise is hollandaise.

The best alternatives to bearnaise are rated as following:
★★★★★  hollandaise
★★  bordelaise
★  hollandaise sauce
  bearnaise
  bechamel

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Speaking about bearnaise, one probably shouldn't forget about chateaubriand.

Other search terms related to bearnaise and their ratings are:
★★★★★ chateaubriand
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Google Trends

Scale is based on the average worldwide traffic of bearnaise in all years. Click on graph for more.
bearnaise
hollandaise
bordelaise