Miley, from Inverurie in northern Scotland, qualified for the 200m medley final as the second fastest behind Hosszu who travelled to Chartres having won 39 races on the World Cup circuit this season.
That saw her pocket nearly $170,000 and she was not prepared to allow Miley, who finished seventh in the 200m medley and fifth in the 400m at the London 2012 Olympics, deny her yet another win.
Hosszu took gold in 2:05.78, less than half a second ahead of Miley, while fellow Hungarian Zsuzsanna Jakabos was third as the three fastest qualifiers for the final took the one-two-three.
Silver represents a marked improvement for Miley having taken bronze in the 200m medley at the European Short Course Championships in 2011 and 2009.
“I’m satisfied with that performance,” said Miley. “I’ve got a busy week ahead and am training through it so to swim so quickly is good.
“I’ve changed my training programme and it’s showing it works. Every season we change things slightly and I’m pleased with the effect it’s had.”
Miley also has her preferred 400m medley, which she won in 2009, to come while the future also looks bright for Britain with 16-year-old Siobhan-Marie O'Connor leading after 100m before dropping to fourth in 2:08.85.
Meanwhile there was joy for Lauren Quigley in the first event of the afternoon session involving a Briton as the 17-year-old just squeezed into the final of the 100m backstroke.
Quigley looked good for most of her semi-final but faded towards the end and placed fourth in 58.44 seconds. However, that was good enough to take the eighth and final qualifying spot.
Karley Mann, who won bronze in the distance at the World Youth Championships last year, could not follow suit though as she finished last in her semi-final in 59.70 and ranked 14th overall.
Antony James failed to make the final of the 100m butterfly for the second successive time at the European Short Course Championships after finishing 13th overall in the semi-finals with 52.23.
However the Commonwealth silver medallist improved on his time and position from last year in Szczecin where he ranked 15th in 52.32.
In the 100m breaststroke semi-finals Craig Benson equalled his position from the heats, finishing 12th to miss out on the final but make a vast improvement on his 38th from last year.
And the final Brit involved on the first day, Lucy Spencer - who was only handed a place in the 100m freestyle semi-finals after Henriette Brekke pulled out - was 14th in 55.22.
Elsewhere Frenchman Yannick Agnel won the first gold medal of the championships in the men's 400m freestyle much to the delight of the home crowd in Chartres.
Agnel set a new world record of 3:32.25 in the 400m freestyle last week but had to be content with 3:37.54 in the final as he edged out Italian duo Gabriele Detti and Andrea Mitchell D'Arrigo.
Radoslaw Kawecki won the men's 200m backstroke in a new championship record of 1:48.51 before Hosszu returned to take a second gold in the space of 15 minutes in the women's 200m butterfly.
Laszlo Cseh beat off home hope Jeremy Stravius to win the men's 200m medley and Olympic men's 50m champion Florent Manaudou added the European Short Course title to his collection.
Petra Chocova won the women's 50m breaststroke while France's men's 4x50m medley relay quartet, including Manaudou, stormed to victory by nearly two seconds and Denmark took the women's 4x50m freestyle title.