Build a complete reference line
Include the company, order or contract number, promised date, last contact, outstanding item, and best callback channel. Send through the vendor's approved business contacts.
State the consequence and required response
Explain the operational impact without threats, then ask for a named action by a reasonable date. Distinguish what the contract requires from what you prefer.
Escalate through legitimate channels
If the deadline passes, use the account manager, support process, procurement team, payment dispute route, or legal advice appropriate to the contract. Do not expose private staff details or harass employees.