Back row ace Mather, who played in Scotland's final three 2003 World Cup matches in Australia, accepts the trip to Watford represents an "immense challenge but we have a lot of young guys in the squad and they won't be overawed, that should stand us in good stead.
"Saracens, like us, have been struggling to find their form but they have some world class players and there is always a good atmosphere at Vicarage Road.
"If we can get a result there, or at least be in close touch, then I believe we will have a good chance in the second leg at Hughenden the following Friday."
Saracens, who have 15 internationals from 10 different countries in their squad, lost out to Bath Rugby on a 6-5 Parker Pen Challenge Cup semi-finals try count last season but their Zurich Premiership win over Leeds Tykes on New Year's Day gave them a timely boost ahead of Glasgow's visit.
"Our Celtic League form has not been the best but this is our last chance of any silverware and, if we can get some momentum going for the rest of the season, that would be great," said Mather.
"We expected a bit more from Montpellier in Round 1, particularly as they were going so well in the French Championship. We would have preferred a sterner test - though we know we will certainly get that against Saracens."
Glasgow: 15 Stuart Moffat 14 Gareth Maclure 13 Graeme Morrison 12 Andrew Henderson 11 Sean Lamont 10 Dan Parks 9 Graeme Beveridge 1 Euan Murray 2 Gordon Bulloch 3 Matt Proudfoot 4 Andrew Hall 5 Nathan Ross 6 Cameron Mather (captain)8 Jon Petrie 7 Donnie Macfadyem
Replacements: 16 Simon Gunn 17 Andrew Kelly 18 Rory McKay 19 Andrew Wilson 20 Sam Pinder 21 Calvin Howarth 22 Rory Kerr