First generate and install an SSL certificate:
    
sudo /etc/init.d/tomcat7 stop
    
$JAVA_HOME/bin/keytool -genkey -alias tomcat -keyalg RSA -keystore ~/keystore
    
sudo mv keystore /etc/tomcat7/keystore
    
sudo chown root.tomcat7 /etc/tomcat7/keystore
    
sudo chmod 440 /etc/tomcat7/keystore
Configure Tomcat properties:
sudo vi /etc/tomcat7/server.xml
Disable the remote shutdown port:
<Server port="-1" shutdown="SHUTDOWN">
Comment out the http connector, enable SSL and specify secure chiphers:
            <!--
            <Connector port="8080" protocol="HTTP/1.1"
                    connectionTimeout="20000"
                    URIEncoding="UTF-8"
                    redirectPort="8443" />
            -->
        <Connector port="8443" protocol="HTTP/1.1" SSLEnabled="true"
               maxThreads="150" scheme="https" secure="true"
               Server=" "
               Secure="true"
               keystoreFile="/etc/tomcat7/keystore"
               keystorePass="the_keystore_password"
               clientAuth="false" sslProtocol="SSL" 
               ciphers="SSL_RSA_WITH_RC4_128_MD5, SSL_RSA_WITH_RC4_128_SHA, TLS_RSA_WITH_AES_128_CBC_SHA, TLS_DHE_RSA_WITH_AES_128_CBC_SHA, TLS_DHE_DSS_WITH_AES_128_CBC_SHA, SSL_RSA_WITH_3DES_EDE_CBC_SHA, SSL_DHE_RSA_WITH_3DES_EDE_CBC_SHA, SSL_DHE_DSS_WITH_3DES_EDE_CBC_SHA" />
Restrict access to the file, and start up Tomcat:
    
sudo chmod 440 /etc/tomcat7/server.xml
    
sudo /etc/init.d/tomcat7 start
Test that the https connection works: https://[host]:8443
This doesn't actually answer your question, sorry about that.