A very important thing to check when deploying an on-premise type of architecture is the networking configuration. Ensure that the Tomcat server is NOT directly accessible outside the server:
When it’s possible, use a secure channel: POP3S instead POP3 (or POP3 over TLS).
You must apply your database engine security best practices.
To check the certificate, you can use openssl. To check active ciphers, you can use nmap:
#!/bin/sh
#
# usage: testSSL.sh remote.host.name [port]
#
REMHOST=$1
REMPORT=${2:-443}
echo |\
openssl s_client -connect ${REMHOST}:${REMPORT} -servername ${REMHOST} 2>&1 |\
sed -ne '/-BEGIN CERTIFICATE-/,/-END CERTIFICATE-/p' |\
openssl x509 -noout -subject -dates
nmap --script ssl-enum-ciphers -p ${REMPORT} ${REMHOST}
You can also use an sslyze python script which does both.
python sslyze.py --sslv2 --sslv3 --tlsv1 --reneg --resum --certinfo=basic --hide_rejected_ciphers --sni=SNI myserver.com