Name the impact without exaggerating it
Describe who had to wait, worry, redo work, spend money, or make a choice with incomplete information. For a message about how to apologize to a customer for a billing error, use this factual base: confirm the order, charge, booking, or service problem and separate verified facts from what is still being checked.
Make repair practical
Offer the repair you can actually complete, with ownership, timing, and any limit stated honestly. Offer the available refund, replacement, correction, or escalation with dates and ownership. Make the immediate next step clear enough that the recipient can answer without reconstructing the entire history.
Let future behavior carry the proof
Do not use empathy as a substitute for a remedy or ask the customer to repeat information you already have. Move payment, privacy, accessibility, and product safety incidents into the documented specialist process immediately. A promise inside a message is weaker than a visible change in what you do after it.