If one travels abroad before Pesaĥ and plans to return home after Pesaĥ, his performance of bedikat ĥametz depends on when he departs: if he departs within thirty days of Pesaĥ, i.e., from Purim onward, he must search his home for ĥametz before leaving. That he will certainly nullify his ĥametz has no bearing, because, as we have learned, the Sages ordained that in addition to bitul ĥametz, one must perform bedikat ĥametz, and since he is still at home within the thirty days before Pesaĥ, the mitzva of bedikat ĥametz already applies to him. Therefore, he must perform bedikat ĥametz on his last night at home. However, he does not say a berakha over this search because it is conducted before the time the Sages ordained for searching (as explained in 3:4 above).
If one leaves home more than thirty days before Pesaĥ, i.e., before Purim, he need not perform a search before he leaves. Then, on Erev Pesaĥ, he must nullify all of the ĥametz in his possession so that he does not transgress by possessing ĥametz. When he returns home after Pesaĥ, he must physically dispose of all of the ĥametz in his home.
However, if at the time of departure one intended to return to his home before Pesaĥ, the Sages ordained that he must perform bedikat ĥametz before leaving, even if he sets out at the beginning of the year. This is because something could go wrong on his journey, preventing him from returning in time for bedikat ĥametz (Pesaĥim 6a, according to Rambam). However, if one appoints a shali’aĥ to search on his behalf on the night of the fourteenth in case he is unable to return in time, he is not required to search before his departure. Nowadays, when one can make a phone call from anywhere in the world, one need not search before setting out on a trip because even if he is unable to return in time for bedikat ĥametz, he can ask a friend or relative to search on his behalf (see Sidur Pesaĥ Ke-hilkhato 12:13).
The poskim differ over what should be done when one was supposed to perform bedikat ĥametz before traveling but forgot to do so. Some say he must return and others say he need not. Therefore, if it is very difficult for him to return, and he cannot find a shali’aĥ to perform bedikat ĥametz for him, he may rely upon his bitul ĥametz (BHL 436:1, s.v. “zakuk”). Then, after Pesaĥ, he must burn or destroy the ĥametz he nullified, because if he derives benefit from it after Pesaĥ, he demonstrates that his nullification was insincere. The same applies any time one nullifies ĥametz but does not remove it – the Sages forbid eating or deriving benefit from it after Pesaĥ (SA 448:5). The best thing to do when one forgot to search his house before traveling is to rent it to a gentile and sell him all of the ĥametz.