If one travels abroad before Pesaḥ and plans to return home after Pesaḥ, his performance of bedikat ḥametz depends on when he departs: if he departs within thirty days of Pesaḥ, i.e., from Purim onward, he must search his home for ḥametz before leaving. That he will certainly nullify his ḥametz has no bearing, because, as we have learned, the Sages ordained that in addition to bitul ḥametz, one must perform bedikat ḥametz, and since he is still at home within the thirty days before Pesaḥ, the mitzva of bedikat ḥametz already applies to him. Therefore, he must perform bedikat ḥametz 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 (above, 3:4).
If one leaves home more than thirty days before Pesaḥ, i.e., before Purim, he need not perform a search before he leaves. Then, on Erev Pesaḥ, he must nullify all of the ḥametz in his possession so that he does not transgress by possessing ḥametz. When he returns home after Pesaḥ, he must physically dispose of all or any significant ḥametz in his home.
However, if at the time of departure one intended to return home before or during Pesaḥ, the Sages ordained that he must perform a bedika 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 ḥametz (Pesaḥim 6a, according to Rambam). However, if one appoints a shali’aḥ to search on his behalf on the night of the 14th 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 ḥametz, he can ask a friend or relative to search on his behalf (see SA 436:1-2; MB 9; SHT 10).
The poskim differ over what should be done when one was supposed to perform bedikat ḥametz before traveling but forgot to do so, and he cannot find someone to do the bedika on his behalf. Thus, if it is very difficult for him to return, he may rely upon his bitul ḥametz (BHL 436:1, s.v. “zakuk”). Then, after Pesaḥ, he must burn or destroy the ḥametz he nullified, because if he derives benefit from it after Pesaḥ, he demonstrates that his nullification was insincere. The same applies any time one nullifies ḥametz but does not remove it – the Sages forbid eating or deriving benefit from it after Pesaḥ (SA 448:5). The best thing for one who forgot to search his house before traveling to do is to rent it to a gentile and sell him all of the ḥametz in it.