Amânar began to excel as an individual performer at the 1995 European Cup, placing second in the all-around behind Svetlana Khorkina of Russia and winning gold on both vault and floor exercise.

Amânar won a silver medal on vault at the 1996 World Championships, behind teammate Gina Gogean and ahead of Cuba's Annia Portuondo-Hatch.

[5] However, in a scenario similar to the Unified Team's substitution of Tatiana Gutsu for Rozalia Galiyeva at the 1992 Olympics,[6] Amânar replaced her teammate Alexandra Marinescu in the all-around final.

[5] The Romanian head coach, Octavian Bellu, said that Amânar deserved to compete because she had worked harder and was a better athlete than Marinescu.

She did not start from a 10.0 in the all-around—despite having the most tumbling bonus points of anyone at the Games—because her tour jeté half-turn (Strug), a C element, was not completed.

Thus, she did not have enough simple A, B, and C skills, and much of her D- and E-rated tumbling had to count as easier elements to fulfill those requirements.

Amânar did not perform a double turn in the team optionals or the all-around because it was not necessary as long as she completed her Strug.

In the event finals, Amânar completed her Strug and added a double turn to fulfill the more stringent Competition III requirements.

Amânar won her only medal of the competition on the floor, taking home the silver behind teammate Andreea Răducan.

[13][14] Initially, Amânar refused to accept the medal, insisting that Răducan had rightfully earned the title.

She married Cosmin Tabără, a lawyer, on 9 March 2002, in Timișoara, and gave birth to a son, Alexandru Iosif, five months later.