While studying sociology, Roel Luynenburg joined the Dutch coxless four with Ruud Stokvis, Eric Niehe and Maarten Kloosterman. At the 1966 World Championships, the quartet earned a bronze medal. After this success, the four split up, with Stokvis and Luynenburg ending up as a coxless pair. The two proved a good duo, and in the 1968 Olympic season, they won the prestigious Rotsee Regatta at Luzern, marking them as a medal favorite for Mexico. On the course at Xochimilco, the duo easily reached the final, but they placed last in the final. A fever for Luynenburg earlier in the tournament combined with the high altitude was too much for them. With the two graduating and getting full-time jobs, their rowing activities in the following years were minimal, but with the 1972 Olympics coming up, the two got back together and qualified their boat again for the Games.
At Munich, the two again reached the final, but this time they contended for the medals. The East German boat was the clear winner, but the Dutch pair battled it out with Switzerland for second place, with Luynenburg and Stokvis eventually placing third. Stokvis retired after this medal, but Luynenburg continued with competitive rowing. In 1975, he won the coxless pairs event at the Henley Royal Regatta (the Silver Goblets & Nickalls’ Challenge Cup) together with Harry Droog. Luynenburg, who worked for a major Dutch bank, also continued to row with Ruud Stokvis, with the duo still being active on the water together well into their 70s.