Conway was one of three on the 16-strong British team for the Europeans to have attended the London 2012 Olympics however only Ashley McKenzie finished on the podium.
He took bronze in the -60kg category while Conway lost her first fight to Anka Pogacnik and Chris Sherrington followed suit against Robert Zimmermann of Germany.
McKenzie and Conway were back for the Baku Grand Slam with the former finishing fifth and the latter this time climbing the podium to collect a bronze medal.
Conway first forced a submission from Croatian Kristina Marijanovic but was then defeated by European bronze medallist Laura Vargas-Koch with a late ippon.
However Conway responded in the bronze-medal match to defeat another German Barbara Bandel with an ippon herself while British teammate Tom Davis was fifth in the -81kg.
And British Judo coach Kate Howey said: "This was a good day for Sally to restore some confidence in herself following the Europeans.
"The result means she has qualified for the (IJF) Masters and goes into it with some strong wins under her belt.
"Tom also fought very well, beating the European silver medallist and fighting the last two contests with an injury. Fifth place here for Tom is an excellent result."
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- Ashley McKenzie