In recent years they've often come up short when their credentials have been laid on the line, although Chelsea circa 2013-14 is a different beast.
The Blues have stepped up to the challenge over the past week or so, keeping up with Arsenal and Manchester City at the top with a draw against the Gunners at Emirates Stadium, while defeating Swansea City and Liverpool.
With rumors continuing unabated surrounding Southampton's Luke Shaw and the Blues, the youngster finds himself in a similar position right now.
The Saints face Chelsea on New Year's Day, providing the perfect opportunity to prove he is capable of succeeding Ashley Cole at Stamford Bridge.
His contract expires in the summer, meaning he will be free to leave Stamford Bridge if a new deal isn't agreed, opening the possibility of him moving to Spain is a very real one.
It's a sign of the times—and they are changing rapidly. Blues boss Mourinho knows that, Cole knows it and while he's remained rather dignified and silent whenever his name has been mentioned with a lucrative transfer, Shaw knows his time to step into the spotlight is fast approaching on the horizon.
The 18-year-old has already given a solid audition in front of Mourinho this term.
When Chelsea defeated Southampton 3-1 in early December, the left-back was probably Saints' Man of the Match. He gave very little away defensively, while he was a major threat in attacking situations.
Given how this Chelsea team appears to be developing—with an emphasis on dynamic attacking play—it was a glimpse as to the role Shaw would fill.
Were that game a test set by Mourinho, the left-back would have passed with flying colors, although Southampton vs. Chelsea on New Year's Day is an altogether different challenge.
In December, Saints were on the crest of a wave. Sitting seventh in the table, they were being talked of as potential challengers for a Europa League spot in the league.
Mauricio Pochettino's team sat above Manchester United and Tottenham Hotspur and were only two points off the top four.
Fast forward a month, the mood is somewhat different. Since that Chelsea defeat, Saints have picked up just five points from their six outings, with a Boxing Day victory over Cardiff City ending a run of six games without a win.
Rather than looking up the table, they're beginning to look behind them as Swansea and Hull City show signs of catching up, pulling Saints into the bottom half of the Premier League.
Things are certainly not as positive as they were, yet for Shaw, the challenges his team face right now give him the chance to flourish.
It's often the notion that we learn less about teams or individuals in times of success. It's when the struggle hits that character is formed and a player shows what he is truly capable of.
Does Shaw have the temperament to perform under scrutiny? Can he help inspire those around him? Does he have the character to impose himself?
Now's the time to answer those questions.
Garry Hayes is Bleacher Report's lead Chelsea correspondent and will be following the club from a London base throughout the 2013-14 season. Follow him on Twitter here @garryhayes