Use certificates that specify OCSP Must-Staple
The Qualys SSL Server Test shows that haveibeenpwned.com uses certificates that do not specify OCSP Must-Staple. When you replace these certificates near their expiry date, please get certificates that specify OCSP Must-Staple. Scott Helme has a good article on why OCSP Must-Staple is important.
https://www.ssllabs.com/ssltest/analyze.html?d=haveibeenpwned.com
https://scotthelme.co.uk/ocsp-must-staple/
TLS termination is done at Cloudflare and this is not a configurable attribute. It poses a minor risk hence the A+ SSL Labs rating HIBP receives.
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That's correct, not without paying a premium. Besides, I've no reason to want to do that.
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Kenneth Barber commented
You can't choose the certificates that your website uses?