Frenulectomy is the removal of the frenulum, and is often done at the same time as a circumcision. For most men this is a purely cosmetic decision. The frenulum exists to draw foreskin back over the glans of the penis, and has no purpose after a circumcision. Having a frenulum does not positively impact sensitivity in any way, because the sensitive nerves stimulated when touching the frenulum are in fact inside the glans, underneath it.

If the aesthetics of retaining or removing your frenulum are not important to you for your circumcision, I recommend having it removed. While the difference is not as profound as removing the foreskin, removing the frenulum has the minor benefit of truly freeing the glans; when it it still attached, the head of the penis is always pulled back and down slightly toward the shaft. Things just feel better without it.

Four and a half years after my circumcision, I removed my frenulum myself, described in this forum post. I have posted images of the results here. I wish I had had it removed during my circumcision, and am absolutely happy that it is gone.