openssl is the command-line program for managing SSL data and certificates.
- To check that a certificate file is valid, and see what it says (does not work with key files) - typical file extensions are .crt, .ca:
openssl x509 -text -in <filename>
- To verify how a web server is presenting its certificate over https:
openssl s_client -connect <domain>:443
- To get the expiration date:
echo | openssl s_client -connect <domain>:443 2>/dev/null | openssl x509 -noout -dates
- To generate a new private key:
openssl genrsa -des3 -out <filename.key> 4096
- To remove the pass phrase from a private key:
openssl rsa -in <oldfile.key> -out <newfile.key>
- There is slightly more explanation here.
- openssl verify  seems to be the tool of choice for checking certificate files stored locally.
- This also has some useful information about using openssl, and a little bit about the "chaining" concept.