For RSA SMIME certificates which are stored on disk it is possible to make a backup copy.
For Brainpool SMIME certificates trying to do this in Kleopatra via right click -> create backup copy first asks for the password and then gives an error ~"export is empty, maybe you gave the wrong password", although the password is correct:

6 - 2023-11-30 15:12:48 gpgsm[8012]: DBG: chan_0x00000258 -> ERR 50331706 Keine Daten <GPGSM>

In case we do not fix this in gpgsm, we should add information in Kleopatra or grey out the option for Brainpool SMIME keys.