The best replacement for websockets is ajax.

The best alternatives to websockets are rated as following:
★★★★★  ajax
★★★★  rest
★★★★  long polling
★★★  socket.io
★★★  xmpp
★★★  sockets
★★★  server sent events
★★  spdy
★★  comet
★★  webrtc
★★  tcp sockets
★  webhooks
  push notifications
  signalr
  bosh

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No companions for websockets have been suggested so far.
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Google Trends

Scale is based on the average worldwide traffic of websockets in all years. Click on graph for more.
websockets
ajax
rest