Although a fine singles player, Bromwich was primarily known as being a particularly good doubles player. Tennis great (and near contemporary) Jack Kramer writes in his 1979 autobiography that if "Earth were playing in the all-time Universe Davis Cup, I'd play Budge and Vines in my singles, and Budge and Bromwich in the doubles. That's what I think of Johnny as a doubles player."

In 1948 Bromwich played the American Bob Falkenburg for the Wimbledon Championship and had match point at 5-3 in the fifth set. He came to the net for a volley but decided that Falkenburg's ball would go long and let it go by. It fell inside the baseline and Falkenburg fought his way back into the match. Bromwich later had a second match point but was unable to win that either and Falkenburg won the championship by winning the last four games of the set for a 7-5 victory. Kramer later wrote that "...it never seemed to me that he was the same player after that. He doubted himself. He was a precision player to start with -- he used a terribly light racket weighing less than twelve ounces, and it was strung loosely. He could put a ball on a dime, and I suppose after he misjudged that one shot, the most important in his life, he never possessed the confidence he needed."

Bromwich gained a measure of revenge against Falkenberg the following year at Wimbledon by defeating him, once again in a five-set match, in the quarter-finals.

Writing about Bromwich, Kramer says, "Bromwich was like McMillan today because as a kid John hit from both sides two-handed, and while he eventually had given up the two-handed forehand, he still hit backhand two-handed and could anything back from the baseline. He had strokes very much like Connors."

Bromwich was inducted into the International Tennis Hall of Fame in Newport, Rhode Island in 1984.