Sample web.config that demonstrates how the previously created web.2.0.config file (https://gist.github.com/sjwaight/7508374) can be updated to support claims-based authentication.

web.4.5.1.config

<?xml version="1.0"?>
<configuration>
  <configSections>
    <section name="system.identityModel" type="System.IdentityModel.Configuration.SystemIdentityModelSection, System.IdentityModel, Version=4.0.0.0, Culture=neutral, PublicKeyToken=B77A5C561934E089" />
    <section name="system.identityModel.services" type="System.IdentityModel.Services.Configuration.SystemIdentityModelServicesSection, System.IdentityModel.Services, Version=4.0.0.0, Culture=neutral, PublicKeyToken=B77A5C561934E089" />
  </configSections>
  <appSettings>
    <add key="ida:FederationMetadataLocation" value="https://localhost/idsrv/FederationMetadata/2007-06/FederationMetadata.xml" />
    <add key="ida:Realm" value="https://localhost/authdemoapp/secured/" />
    <add key="ida:AudienceUri" value="https://localhost/authdemoapp/secured/" />
  </appSettings>
  <connectionStrings>
    <!-- you'll need to change this to match your server - the one below is using the default local instance with Windows Auth. -->
    <add name="aspnetmembers" connectionString="server=.;initial catalog=AuthDemoApp;Integrated Security=SSPI"/>
  </connectionStrings>
  <system.web>
    <httpRuntime targetFramework="4.5" requestValidationMode="4.5" />
    <compilation debug="true" targetFramework="4.5.1"/>
    <authentication mode="None"/>
    <roleManager defaultProvider="SqlProvider" 
                 enabled="true" 
                 cacheRolesInCookie="true" 
                 cookieName=".ASPROLES" 
                 cookieTimeout="30" 
                 cookiePath="/" 
                 cookieRequireSSL="true" 
                 cookieSlidingExpiration="true" 
                 cookieProtection="All">
      <providers>
        <add name="SqlProvider" 
             type="System.Web.Security.SqlRoleProvider" 
             connectionStringName="aspnetmembers" 
             applicationName="AuthDemoApp"/>
      </providers>
    </roleManager>
    <pages controlRenderingCompatibilityVersion="3.5" clientIDMode="AutoID"/>
  </system.web>
  <system.webServer>
    <modules>
      <add name="WSFederationAuthenticationModule" type="System.IdentityModel.Services.WSFederationAuthenticationModule, System.IdentityModel.Services, Version=4.0.0.0, Culture=neutral, PublicKeyToken=b77a5c561934e089" preCondition="managedHandler" />
      <add name="SessionAuthenticationModule" type="System.IdentityModel.Services.SessionAuthenticationModule, System.IdentityModel.Services, Version=4.0.0.0, Culture=neutral, PublicKeyToken=b77a5c561934e089" preCondition="managedHandler" />
    </modules>
  </system.webServer>
  <system.identityModel>
    <identityConfiguration>
      <audienceUris>
        <add value="https://localhost/authdemoapp/secured/" />
      </audienceUris>
      <securityTokenHandlers>
        <add type="System.IdentityModel.Services.Tokens.MachineKeySessionSecurityTokenHandler, System.IdentityModel.Services, Version=4.0.0.0, Culture=neutral, PublicKeyToken=b77a5c561934e089" />
        <remove type="System.IdentityModel.Tokens.SessionSecurityTokenHandler, System.IdentityModel, Version=4.0.0.0, Culture=neutral, PublicKeyToken=b77a5c561934e089" />
      </securityTokenHandlers>
      <certificateValidation certificateValidationMode="None" />
      <issuerNameRegistry type="System.IdentityModel.Tokens.ValidatingIssuerNameRegistry, System.IdentityModel.Tokens.ValidatingIssuerNameRegistry">
        <authority name="http://identityserver.v2.thinktecture.com/trust/claimsdemo">
          <keys>
            <add thumbprint="42458679ECD5F89F51FD126BE3F2F4408464C936" />
          </keys>
          <validIssuers>
            <add name="http://identityserver.v2.thinktecture.com/trust/claimsdemo" />
          </validIssuers>
        </authority>
      </issuerNameRegistry>
    </identityConfiguration>
  </system.identityModel>
  <system.identityModel.services>
    <federationConfiguration>
      <cookieHandler requireSsl="true" />
      <wsFederation passiveRedirectEnabled="true" issuer="https://localhost/idsrv/issue/wsfed" realm="https://localhost/authdemoapp/secured/" requireHttps="true" />
    </federationConfiguration>
  </system.identityModel.services>  
</configuration>