> and how do I generate an ECDSA certificate?

To generate a selfsigned ECDSA cert the same ways you do RSA, 
except use EC instead of RSA.

- use req -new with EC key or -newkey with EC parms and -x509 
to generate selfsigned cert directly.

- use req -new with key or -newkey to generate CSR,
then x509 -req -signkey to create selfsigned cert

Set other attributes as appropriate. If you set KeyUsage,
it must include digSign to use this cert for ECDHE-ECDSA.
(KU for RSA should include digSign or encrypt depending 
on the suites to be used, but sometimes isn't enforced.)

Use a curve supported by the peers you will communicate with.

To obtain a CA-signed ECDSA cert the same ways as RSA,
except EC instead of RSA, and harder.

- generate CSR for EC key as above, for suitable curve

- find a CA that issues EC certs, with usage allowing 
at least digSign=ECDSA. I haven't found any yet.

- submit CSR to CA, prove your identity, pay fees.

- receive cert and any chain cert(s) from CA. 

<snip>

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