Intel SGX comes with an attestation process aiming at exactly that. The attestation contains a number of details, such as the hardware configuration (cpu microcode version, BIOS, etc) and the hash of the enclave code. At system startup the CPU gets a certificate from Intel confirming the configuration is known safe, which is used by the CPU to in turn certify the enclave is indeed running code with a given fingerprint.
When the connection is established we verify the whole certificate chain up to Intel, and we verify the TLS connection itself is part of the attestation (public key is attested).
When the connection is established we verify the whole certificate chain up to Intel, and we verify the TLS connection itself is part of the attestation (public key is attested).