Courier website says delivered but buyer insists it not been received.

[horseshoe]

What do I do now??

Should I issue a refund?

Contact the courier and find out what has happened.. make sure you speak to somebody! the courier insurance will have to cover it

Ask courier for proof of delivery - eg signature - get a hard copy not just an email. Inform buyer that courier says it has been delivered and you are requesting proof to keep them in the loop, lots of good communication.
Could be courier delivered to wrong address, another household member signed & hasn't told buyer, unscrupulous delivery driver forged signature..........

We had this problem (as a buyer). The courier had delivered to a road name similar to ours and some hooky character had signed for the stuff. It was a £50 hard drive, so I wasn't too happy, but between us (customer and seller) we hounded the couriers til they sorted it out.

The seller actually sent a duplicate item and we stayed by window waiting for them to come. When they didn't arrive, we rang them up and they said they'd attempted delivery....no-one home. That was when we asked them to recheck the address and sure enough it was wrong!

I know how frustrating this one is from both the seller and the buyers point of view and I hope you manage to sort it out!