The best replacement for shibboleth is openid.

The best alternatives to shibboleth are rated as following:
★★★★★  openid
★★★★  cas
★★★  adfs
★★★  oauth
★★★  saml
★★  openam
★★  simplesamlphp
★  jasig cas
★  ezproxy
★  josso
★  shibboleth
★  pubcookie
★  openathens
  opensaml
  opensso
  picketlink
  athens

Your alternative for shibboleth is not listed? Suggest!
Speaking about shibboleth, one probably shouldn't forget about cas.

Other search terms related to shibboleth and their ratings are:
★★★★★ cas
You have in mind a companion for shibboleth and it is not yet here? Propose!



Google Trends

Scale is based on the average worldwide traffic of shibboleth in all years. Click on graph for more.
shibboleth
openid
cas