If you have a tubal ligation can you still get pregnant?
Artificial methods will work and are used for women with naturally blocked tubes (which is quite common) - the techniques for extracting eggs, perfoming 'in vitro' fertilisation and implantation are effective, if rather expensive. (Test tube babies)
There is less than a half a percent chance of getting pregnant after tubal ligation. In other words, for every 200 people that get tubal ligation done, one will be able to become pregnant. It is possible, but it is not probable, particularly if you have been having unprotected sex with a husband this entire time, and have not gotten pregnant until now.