The Intimidation skill in Savage Worlds provides some clearly defined mechanics for combat situations, but the rules state only that "more subjective effects are determined by the Game Master in roleplaying situations". That is a very open ended statement, and I've yet to see anything more clearly defined, so for inspiration I decided to take a look at the Intimidate skill in D&D, as it works in a roughly similar sort of way during combat (you make an opposed roll against your foe, if you win they become shaken for a round).
When used outside of combat, the D&D Intimidate skill requires 1 minute of interaction as well as a successful opposed roll. If you win, your target's attitude is treated as "Friendly" while they remain in your presence and for d6*10 minutes afterwards, but their default attitude shifts to Unfriendly (or Hostile, if they were already Unfriendly).
Note that the five D&D attitudes are "Hostile", "Unfriendly", "Indifferent", "Friendly" and "Helpful", and they are very close parallels with the five Savage Worlds attitudes of "Hostile", "Uncooperative", "Neutral", "Friendly" and "Helpful". These attitudes can normally be increased in D&D by way of the Diplomacy skill, which works very much like Persuasion in Savage Worlds. Although the two systems are obviously different in many ways, and great care should be taken with direct comparisons, these particular skills work similarly enough to provide a good frame of reference.
Savage Worlds encourages the GM to apply situational modifiers to Intimidation rolls, giving the example of "waving a gun in someone's face" as being "definitely worth a +2 bonus" unless they have a bigger gun of their own. From there one could extrapolate that waving a knife in someone's face might be worth a +1 bonus, while resorting to extreme methods (such as torture, or threatening to kill a loved one) might be worth +4.
That same bonus could be turned into a penalty if the situation were reversed, for example threatening someone who is holding a knife while you're unarmed might incur a -1 penalty. Similarly, forcing someone to give you their credit card and PIN might incur a -1 or -2 penalty, while forcing them to tell you the safe house where their family members are hidden (when they know you mean their family harm) would probably incur a -4 penalty.
Proposed Usage Guidelines
Based on my above observations, my suggestion for handling Intimidation outside of combat is as follows:
It requires at least 10 rounds (1 minute) of interaction to intimidate your target into cooperating. Make an Intimidation roll, they may attempt to resist with an opposed Spirit roll. If you beat them, they cooperate as if their attitude were "Friendly" for as long as they remain in your presence, and for up to half an hour afterwards, increased to an hour if you beat them with a raise. However their default attitude towards you becomes Uncooperative, or Hostile if they were already Uncooperative. Modifiers should be applied by the GM based on the methods you use and the services or information you require from your target.