To ensure the security of your SIP trunks with Twilio, enabling Secure Trunking is crucial. This feature can be secured by flipping a switch on the Elastic SIP trunk, and it's now available for free. To configure a Cisco Unified Border Element (CUBE) with TLS & SRTP, you'll need to generate an RSA key, create a PKI trustpoint, import the Digicert global root CA certificate, set up SRTP auth cipher, create a dspfarm profile, update sip-ua settings, and finally enable STRP & TLS on the dial-peers facing Twilio. Troubleshooting common issues can be done by using debug commands such as `debug ccsip messages`, `debug crypto pki validation`, and `debug ssl openssl errors`. By following these steps and troubleshooting tips, you'll be able to secure your SIP trunks with Twilio and ensure the integrity of your communication network.