First of all, I hope you are not using OpenSSL1.0.1 on your server because it is vulnerable to HeartBleed.
Before answering your question, let us see some of the main elements in an X.509 certificate (from RFC 5280):
Certificate
Version
Serial Number
Algorithm ID
Issuer
Validity
Not Before
Not After
Subject
Subject Public Key Info
Public Key Algorithm
Subject Public Key
Issuer Unique Identifier (optional)
Subject Unique Identifier (optional)
Extensions (optional)
You can notice by yourself that all the elements remain the same. If you do not change the key and the algorithm you used then the certificate is still valid.
I mean you do not need to issue an other certificate since all the cipher suite of OpenSSL0.9.8 exist in your ne OpenSSL version which has, in addition, this list:
TLS_ECDHE_ECDSA_WITH_CAMELLIA_128_CBC_SHA256 ECDHE-ECDSA-CAMELLIA128-SHA256
TLS_ECDHE_ECDSA_WITH_CAMELLIA_256_CBC_SHA384 ECDHE-ECDSA-CAMELLIA256-SHA384
TLS_ECDH_ECDSA_WITH_CAMELLIA_128_CBC_SHA256 ECDH-ECDSA-CAMELLIA128-SHA256
TLS_ECDH_ECDSA_WITH_CAMELLIA_256_CBC_SHA384 ECDH-ECDSA-CAMELLIA256-SHA384
TLS_ECDHE_RSA_WITH_CAMELLIA_128_CBC_SHA256 ECDHE-RSA-CAMELLIA128-SHA256
TLS_ECDHE_RSA_WITH_CAMELLIA_256_CBC_SHA384 ECDHE-RSA-CAMELLIA256-SHA384
TLS_ECDH_RSA_WITH_CAMELLIA_128_CBC_SHA256 ECDH-RSA-CAMELLIA128-SHA256
TLS_ECDH_RSA_WITH_CAMELLIA_256_CBC_SHA384 ECDH-RSA-CAMELLIA256-SHA384
To answer to your question raised via your comment to the other answer, a certificate is used simply to prove that you own the public key you pretend it is yours.