Kawaja moved to Ontario as a youth, and became a high profile skip (he won the 1980 Ontario junior championship), but it was not until his move to the Ed Werenich rink that he finally started to win championships.
In 1983, Kawaja won his first provincial championship, playing second for Werenich. The team not only won the provincial championship, but they won the Brier and the World Curling Championship as well that year. Kawaja is the youngest player to have ever won the Canadian Championship (21 years old)
In 1984, the team repeated their provincial championship, but lost in the Brier final to Michael Riley's Manitoba rink.
Kawaja was promoted to the third position for Werenich, and in 1990 won his third provincial title. The team followed up with another Brier and World Championship.
Kawaja won two more provincial titles with Werenich in 1995 and 1997. He and Ed Werenich formed the nucleus of teams that won more money than any curling team in the 1980s and 90's.
Kawaja retired from curling in January 1998, and now resides in San Diego, California. He is an executive with the Taylormade golf company.