Jonathan Berry began helping to run tournaments in his mid-teens. He was in Mexico in 1973 on vacation when he was asked to direct the Mexican Zonal qualifier, which he did successfully. He successfully ran the first Pan-American Individual Championship at Winnipeg, Manitoba, 1974, where his bilingual skills in English and Spanish proved very helpful. He directed the 1974 Canadian Junior Championship in Vancouver. Berry directed Vancouver 1975, an International tournament with 320 players, which was won by Paul Keres; it was Keres' last victory before he died a few weeks later. Based upon those four major events, Berry was awarded the title of International Arbiter by FIDE in 1975, at the age of only 22, the youngest ever (a record since broken).

Berry directed the Grand Manan International 1984. He also became involved at the Olympiad level later that same year, in Thessaloniki. He has returned to the Olympiad in 1996 Yerevan, 2000 Istanbul, and 2004 Calvia. The 1988 World Chess Festival, Saint John, New Brunswick, was by far the grandest chess event ever held in Canada; it had seven Candidates' matches, two strong International Opens, several Class tournaments, and the World Blitz Championship. Berry was an assistant arbiter for the Candidates' matches. Berry helped to run the 1988 World Rapid Championships in Mazatlan. From 1994-99, Berry was the head Arbiter for the North Bay International Open series of six tournaments, which averaged over 250 players. Berry was the head arbiter for the 25th anniversary Paul Keres Memorial Tournament, Vancouver 2000. Berry was an assistant arbiter at the U.S. Chess Championship, Seattle, in 2002 and 2003.

He has been in charge of three Canadian Open Chess Championship: at Winnipeg 1986; at Kapuskasing 2003 (where he introduced an innovative pairing system, the 'Kap' system); and at Ottawa 2007, which saw a record 22 Grandmasters participate, and where he utilized the "Capelle la Grande" pairing system, its first use in Canada. Berry is Canada's most experienced arbiter, both in length of service and in variety of top events run. However, Berry has drawn some criticism in certain circles, for introducing incredibly complex pairing systems which are often difficult for participants to understand.