The best replacement for h61 is h77.

The best alternatives to h61 are rated as following:
★★★★★  h77
★★★★  h67
★★★  z77
★★★  h81
★★★  b75
★★★  z68
★  b85
★  g41
★  h87
★  h71
★  b75 chipset
★  p61
★  q77
★  z77 chipset
  p67
  h67 chipset
  z68 chipset

Your alternative for h61 is not listed? Suggest!
Speaking about h61, one probably shouldn't forget about ivy bridge.

Other search terms related to h61 and their ratings are:
★★★★★ ivy bridge
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h61
h77
h67