Q. After a woman gives birth, does she bench Hagomel or can her husband say Hagomel for her.
A. On question 610 we wrote: Shulchan Oruch (O.H. 223: 1) rules that when a son is born one recites Hatov Vehametiv. For a daughter Mishna Berura (ibid.) suggests to recite shehecheyanu.
Some have the minhag to recite hagomel after ones wife gives birth or when the yoledes attends shul for the first time. (Mishna Berura 219: 17).
Even when the case warrants reciting Hagomel, if women recite this brocho is debatable, since it has to be said in the presence of a minyan of men. Sephardic women in general do. (Birkei Yosef 219: 2, Kaf Hachaim ibid. 3, Ben Ish Chai P. Eikev 8, et. al.).
Ashkenazim however, differ in their minhagim, but mostly dont. (Piskei Teshuvos 219: 10). In regards to a woman giving birth or after ones wife gives birth, when the yoledes attends shul for the first time, some have the minhag that the husband recites Hagomel and has her in mind (Mishna Berura 219: 17 see question 610).
Horav Shlomo Miller’s Shlit’a opinion is that usually women dont recite this brocho in chutz laaretz and it suffices if they come to shul and recite with kavanah a Tehilim Mizmor of praise and thanks to Hashem.
Rabbi A. Bartfeld as advised by Horav Aharon Miller Shlit’a