The best replacement for saml is openid.

The best alternatives to saml are rated as following:
★★★★★  openid
★★★★  oauth
★★★  ldap
★★  xacml
★★  ws-federation
★★  sso
★★  cas
★★  kerberos
★  jwt
★  oauth 2
★  openid connect
★  spml
  x.509
  ws-security
  oath
  saml2
  ntlm
  shibboleth
  ws

Your alternative for saml is not listed? Suggest!
Speaking about saml, one probably shouldn't forget about spring security.

Other search terms related to saml and their ratings are:
★★★★★ spring security
★★★★★ adfs
★★ datapower
★ sso
You have in mind a companion for saml and it is not yet here? Propose!



Google Trends

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