How do you handle a frustrated user or stakeholder during a technical problem?

The skill is de-escalation without over-promising.

• Acknowledge the impact first, before explaining anything. People need to know you understand what it is costing them. Leading with technical detail reads as deflection.
• Never be defensive, even when the cause is on their side. Assigning blame during an incident helps nobody.
• Give a realistic timeline, or say honestly that you do not have one yet and commit to an update time. "I do not know the cause yet, I will update you at 3pm" is far better than an optimistic estimate you will miss.
• Offer a workaround where one exists. Partial function restored buys enormous goodwill.
• Follow up after resolution to confirm it is genuinely fixed and explain briefly what happened.

Note: The strongest version of this answer includes recognising when frustration is legitimate — the same problem recurring, or a known issue never fixed. In that case the right response is to escalate for a permanent fix rather than to manage the person's feelings. Interviewers value someone who advocates for users rather than only placating them.