Fiorentina, who lost to Real Madrid in the second European Cup final in 1957, won the first edition of the now-defunct Cup Winners' Cup in 1961. They lost in the final the next season and lost to Juventus in a two-legged UEFA Cup final in 1990.
West Ham won the Cup Winners' Cup in 1965 for their only moment of continental glory. They lost in the 1976 final and the closest they have come since, excluding the 1999 Intertoto Cup victory, was last season's Europa League semi-finals.
Overcoming that agonising defeat by Frankfurt has been a driving force for the east London club this season, particularly once their Premier League survival was assured.
"I do believe the players have got a great opportunity to be remembered by everyone at this club," West Ham manager David Moyes said when asked to compare the current side with the 1965 group that included Bobby Moore, Geoff Hurst and Martin Peters, who helped England win the World Cup a year later.
"I don't know if we will ever get a statue as we are talking about three English legends as well as West Ham legends, but there is a new generation of young supporters developing in the East End of London. If we can give them something to believe in, that they can reach a final, win finals, it would be nothing but positive.
"We have got a really good group, strong international players, players who are hungry to succeed. I hope we can show that on Wednesday."
Forward Jarrod Bowen, who played in the semi-finals last season, said Wednesday's match in Prague would be the biggest of his career.
"I’ve played for England, but I think achieving this with your team-mates who you’ve been with together to get to a final and you have the opportunity to win a trophy together, it will be a massive moment and for the fans it would mean so much," he said.
Fiorentina finished with a bit of a flourish in Serie A, winning nine and drawing four of their last 15 games to end up eighth in the standings as coach Vincenzo Italiano took the opportunity to shuffle his squad.
They have been at their attacking best though in Europe, banging in 38 goals in their 16-game journey to the final.
Italiano raised some eyebrows last week when he said he had instructed his players to think about tactical fouls to cut down the danger of West Ham's counter-attacks
"We know their qualities, we hope that we have found some weak spots and to exploit them in the final," he said. "We need to be very respectful, we need to play a very cautious game."
Fiorentina qualified for the final after Antonin Barek's goal deep into stoppage time of extra time clinched a 3-1 win at Basel to secure a 4-3 aggregate victory.
Italiano says his team's progress from the playoff round back in August has been built on the three principles of courage, drive and adaptability. "We showed these qualities in every game (in the competition)," he said.
"Even more so in the last few fixtures, particularly in that last game against Basel. With grit and a good strategy we managed to overturn the first-leg deficit to qualify for this final."
