Magnolia 5 isn't currently supporting session clustering, that is distribution of the Magnolia web app across multiple Java VMs. This would entail making most of the UI serializable which is a huge effort we decided to postpone after 5.5 (more details at https://wiki.magnolia-cms.com/display/DEV/Serialization+issues).
It was instead decided to suppress the useless (and somewhat alarming) java.io. NotSerializableException in logs (see related issue). This is done by default in our Tomcat bundle starting from versions 5.4.8 and 5.5. There are however other containers which need documentation on how to do it, most notably Websphere and Weblogic. I'll try to find the relevant pages in their documentation (tried with Websphere but got lost).

Tomcat: http://tomcat.apache.org/tomcat-6.0-doc/config/manager.html#Disable_Session_Persistence which is what is done by default in our bundles as of 5.4.8 and 5.5
WebLogic: apparently sessions are not persisted by default. See persistent-store-type at https://docs.oracle.com/cd/E13222_01/wls/docs92/webapp/weblogic_xml.html and https://docs.oracle.com/cd/E13222_01/wls/docs92/webapp/sessions.html
WebSphere: apparently one needs to go to Application Servers -> ServerName -> Session Management -> Distributed environment settings and in the Distributed session properties tab choose None https://www.youtube.com/watch?v=x0Xg8RTB7T0 and http://www.ibm.com/support/knowledgecenter/SSEQTP_8.0.0/com.ibm.websphere.base.doc/info/aes/ae/tprs_cnfs.html