The Mishna requires one to do pidyon ha'ben to a child who lived passed day 30, but then died. Tosafos questions whether one should make a bracha of shehechiyanu when performing pidyon ha'ben on a dead child. The Birkas Shmuel (Kiddushin #18) points out that the only rationale that Tosafos has not to say Shehechiyanu is that there is pain associated with it due to the child's death, but the implication is that the mitzvah is in full force as if the child was still alive and therefore shehechiyanu may be appropriate. The difficulty with this is that the Rivash explains in a teshuva (131) that the language for the bracha on pidyon ha'ben is "על פדיון הבן" rather than "לפדות". He explains that this fits well with the Rambam (Brachos 11:12) who says that anytime the mitzvah is done for someone else i.e. separating teruma one someone else's grain, or hanging a mezuza in someone else's house, the bracha should be על. Therefore, when one performs pidyon ha'ben for himself, the bracha should be לפדות, but when he performs it for his son, since it is primarily the son's obligation that the Torah requires the father to perfrom, the bracha should be על. The Birkas shmuel asks that the Rambam (11:10) says that shehechiyanu is made when one is doing their mitzvah, not when one is doing the mitzvah of someone else. If we regard pidyon ha'ben as the son's mitzvah, not the father's, hence the bracha is made using the term על, there shouldn't be any shehechiyanu. From Tosafos we find that not only is shehechiyanu made on a standard pidyon ha'ben that the father does for the son, but even after the son dies, the bracha of shehechiyanu is made. It would seem that after the son has died we can no longer say the father is performing the mitzvah for his son, because there is no obligation on a deceased person to do any mitzvah. The fact that the father performs the mitzvah after the son's death and makes the bracha of shehechiyanu, implies that the obligation of the father to redeem his son is primarily the father's own obligation, not merely something the Torah requires him to do for his son. The Birkas Shmuel points out that this directly contradicts the Rivash.
The Birkash Shmuel explains that the obligation for a father to do pidyon ha'ben after his son has died is not to fulfill a mitzvah obligation, rather the debt that was created by the mitzvah before the son had died must still be paid. It is a monetary obligation rather than a mitzvah obligation. However, he suggests that although there is no longer a mitzvah obligation on the father since the son has died (and we are assuming like the Rivash that the primary mitzvah is on the son), there is still a kiyum mitzvah, a fulfillment of a mitzvah that is achieved by the father doing pidyon ha'ben on the deceased son. Now, the bracha of shehechiyanu is different than the bracha of על פדיון הבן in that the bracha of shehechiyanu is on the joy one receives from the opportunity to fulfill a mitzvah. Even on a kiyum mitzvah the bracha of shehechiyanu is appropriate. But a birchas ha'mitzvah is a bracha on the chiyuv, not on the kiyum, as the text of the bracha indicates וצוונו על פדיון הבן. Since the primary chiyuv is on the son, just that until he is 13 the Torah places that obligation on the father to fulfill his son's mitzvah, the language of the bracha is על פדיון הבן since the primary obligation is on the son, not the father. But regarding the shehechiyanu which is on the kiyum ha'mitzvah, the father is certainly fulfilling a mitzvah and can therefore make shehechiyanu. Following this approach it should follow that when a father does pidyon ha'ben after the son had died, since there is a monetary obligation to pay a debt but no longer a mitzvah obligation since the son is dead, there shouldn't be any birchas ha'mitzvah at all. The Birkas Shmuel points out that someone asked him this question, but he was pushed off the question saying that since at some point there was an obligation, even though now it is only a kiyum, the bracha may still be made. But for shehechiyanu, if it were made for a chiyuv mitzvah, it would not be made at all when there is no chiyuv. The fact that Tosafos says it is made after the son's death indicates that it is made for a kiyum mitzvah even when there is no chiyuv.