On Stop 6 of the tour - the third consecutive day of action - the men missed out on the final by a point after the three teams in their group all recorded a win each, while the women ran the USA close.
The GB Men - Flynn Boardman-Raffet, Veron Eze, Eljay Morris and Evan Walshe - pipped Israel 21-19 with a winner from Walshe.
After that they fell just short in an entertaining battle with the Netherlands, going down 18-14.
"I'm really proud of the guys. To beat Israel, who won the stop yesterday, was a great achievement!
"The group of players over both tournaments have grown and improved. The men have shown they are right there and ready to take a stop win! If we continue in this trend the next few years will be a exciting one for GB 3x3.”
After two tough days, the GB Women fought hard and put in two better performances but couldn't quite grab a W.
Paige Robinson, Loren Christie, Katie Bennett and Ebony Horton took the USA close, eventually losing out 19-17 before going down 18-11 to Israel.
"We took another step in the right direction, opening the day by pushing the USA to within one basket. The goal out of these stops was to learn how to complete in this different format and find out how far away we are from the nations that are making it a priority.
"We improved through every stop again and I believe we could succeed in this format."
The teams were entered as part of a collaboration between Great Britain Basketball and Basketball England to help prepare Team England players for next year’s Commonwealth Games and set about improving the GB national teams’ 3x3 rankings.