Q. If the father searches for chometz and the son burns it next day, who recites the bracha of Al biur Chametz, the father since he owns the chametz or the son who actually burns it?

A. The Brocho is made for the bedika and the subsequent burning of the chometz. However, as the Rema rules (O.H. 432: 2), and the Mishna Berura (ibid 13) explains and maintains in the name of the Achronim, even if one did not find any chometz at all, it is not a brocho in vain, since he did the perform the required bedika after all.
Therefore, Horav Shlomo Miller Shlit’a explains, the father should recite the brocho “al biur chometz”, since he is doing the bedika. He should ask his son to join him and listen to the brocho with the intention of performing the biur or burning next day (and helping in the search). He should also appoint him as his shaliach or agent for the burning of the chometz next day.

Rabbi A. Bartfeld as revised by Horav Shlomo Miller Shlit’a