Florida State (2015–2017)

In the fall of 2015, Cardama Báez enrolled at Florida State University to compete for the Florida State Seminoles.

She made her NCAA debut on 4 September, finishing third at the Covered Bridge Open in Boone, North Carolina. She would end her first NCAA cross country season finishing ninth at the ACC Championships and eleventh at the South Regional.^[4]

In June 2016, Cardama Báez won the Spanish U23 Championship in the 5000 m and represented Spain at the Mediterranean U23 Championships in Tunis, finishing fourth.

During the 2016 cross country season, Carmela would improve her position at the ACC Championships and South Regional placing seventh and third respectively. This qualified her for the national meet in Terre Haute, Indiana where she finished 73rd.

Cardama Baez would go on to place fourth at the 2017 ACC Championships indoors and out, running a 16:07.49 personal best in the former.

Oregon (2017–2021)

For the 2017 cross country season, Cardama Báez transferred to the University of Oregon to compete for the Oregon Ducks. She debuted for Oregon on 29 September 2017 placing twelfth at the Dellinger Invitational. At the Pac-12 Championships on 27 October, she placed 23rd and went on to finish 34th at the NCAA championships.

Indoors, in 2018, Cardama Báez ran personal bests over 3000 m (9:23.48) and 5000 m (15:55.00). Outdoors, she would make her debut over 10000 m, running 33:36.73 at the Stanford Invitational and finishing fourth at the Pac-12 Championships a month later in 33:24.39.

In fall 2018, Carmela would improve upon her previous performances to finish 8th at the Pac-12 cross-country championship and 31st at the national meet. On 9 December, she placed 8th at the European Cross Country Championships in the U23 race.

Cardama Báez opened her 2019 track season with a 32:55.50 personal best over 10000 m at the Stanford Invitational. A month later at the Stanford Payton Jordan Invitational, she would run a 15:38.77 5000 m personal best in the 5000 m. She qualified for nationals in both events but chose to just contest the 10000 m at the championship. In Austin, at the 2019 NCAA Division I Outdoor Track and Field Championships, she would place second, to New Mexico's Weini Kelati. A month later, she competed at the European 10,000 m Cup in London, running a 32:26.43 personal best and finishing sixth.

On 7 December, Carmela set a Spanish indoor 5000 m record of 15:25.41 in Boston, setting a 13-second personal best in the process.

On 14 May 2021, Cardama Báez won the Pac-12 10000 m title in Los Angeles beating the field by over 10 seconds. The next month at the NCAA Championships in Eugene, she won her first NCAA title, running a 32:16.13 personal best in the process.^[5]