Kamyuku recorded 25:54, improving on his initial best of 26:40 in the men's 60m freestyle on Thursday while Paxinos broke her best time of 30:60 by clocking 29:91 in the women's 50m freestyle on Friday.
Both did not qualify for the next stage even though Paxinos finished second in her heat while Kamyuku was sixth.
The qualification depends on the top 16 times recorded. Speaking to Monitor Sport on Saturday, Paxinos said that she is feeling great about her performance at her first Olympic competition."The experience I got here alone is amazing and I am very proud of myself.
"I worked very hard so that I put up a very good performance and I am very happy," she said. She is now focused on the next competitions between now and January next year where she will use her personal experience in the Olympics to improve and perform better.
Botswana's swimming coach, Allison La Goange praised the swimmers for their achievements. "We are very proud of them. They did very well and it has been a tremendous experience for them.
"They can only get stronger," she said. La Goange stated that the two swimmers' experience will be vital in their preparations for the next Olympics.
She said that after the Olympics, the swimmers will be taking part in regional and international competitions. She added that the two athletes are very happy for being part of the Olympics and representing the country at the world's biggest sporting event.
Swimming is not one of the most popular sports in the country. But the performance of Paxinos and Kamyuku may be enough to convince other youngsters in the country that just like football, volleyball, boxing and karate, swimming is an important sport.
Both Paxinos and Kamyuku were initially not part of the Olympic team but were later picked through the wild card.