A while ago I had to renew the SSL certificate for a website I'm taking care of.

How do I verify that a private key matches a certificate?

openssl x509 -noout -modulus -in server.crt | openssl md5
openssl rsa -noout -modulus -in server.key | openssl md5

How do I verify that a CSR matches a certificate match?

openssl req -noout -modulus -in server.csr | openssl md5