Driver McNeil told BBC Sport: "It means so much, I've been working really hard for a long time so - to finally have a medal, which is all I wanted from the start, is great.
"My first run wasn't great, I wasn't pleased with it at all as I'd done better in training. So for the second one I just had to forget everything, pretend it's a new race, a new day. We pushed our best, I had a fairly good drive and it worked out in the end."
DID YOU KNOW?
“Britain have won four Winter Olympics medals in bobsleigh - the last one in the four-man bob in 1998”
Brakewoman Sawyers, who won athletics gold medals in long jump and 4x100m relay at the Youth Commonwealth Games in 2011, added: "This is what we came here really hoping we could get and after the first run we were fourth, thinking we haven't done it.
"We then thought we'd got third and then looked at the last sled and realised we had silver. It feels amazing."
British Olympic Association chief executive Andy Hunt predicted a bright future for the duo, who won on the track where Britain triumphed in two-man bobsleigh at the 1964 Winter Olympics.
He said on Twitter: "Mica McNeil & Jazmin Sawyers win bobsleigh silver. Brilliant, no doubt Innsbruck is just the start for these two!"
In the boys bobsleigh, GB's Olly Bidulph and James Lelliott came fifth, 0.27 seconds behind gold medallists Patrick Baumgartner and Alessandro Grande from Italy and 0.10 seconds off a medal.
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