You've asked a question where there are about a million possible solutions, none of which will work all the time, some which will work better than others, and some which will never work. I'll just focus on what I believe will work, plus a couple danger points to avoid.
Here's some required reading on the subject of manager-employee communication and relationships:
No matter what...
If you are thinking about putting them together in a room, absolutely always talk to each first. Otherwise, you're essentially putting two volatile chemicals together completely blind. The only thing you know is that the two parties are likely to react -- but you don't know how, why, or what can sooth them.
When you talk to them first, try to get a feel for:
- The story
- The back story (what led up to it)
- The history (the baggage)
- Their values (as Wesley Long mentioned)
- What they want out of the situation
- What they really need out of the situation (like a customer, what they need and what they think they need are often very different things).
If it's not a "blow-up" yet...
If this problem has not blown up to the point that you know you've got some smoothing to do on each side...
Bob complains to you that Alice is never helping out. Alice has no idea that Bob complained or is annoyed.
... then I would consider resolving this entirely in your own one-on-ones. At this point, you don't really stand to gain much by placing one person in defense against their accuser.
This situation mostly presumes that the "defendant" mostly had good intentions but by nature of some personality flaw (in either party) or miscommunication, has upset another person.
In your one-on-ones, I'd recommend discussing the values of your team (standard community values like "Assume good faith", "Be kind", etc. as well as whatever specific values you have).
First visit with the party that has the problem. I would take the approach of listening more than talking, and letting the employee talk themselves into a good solution. It's quite possible the conflict can disappear here.
If there is a need for you to address the behavior of the other person, for reasons such as:
- The reporting/complaining party can't fix it on their own
- Many different people have complained of the same behavior
... then have the one-on-one with the problem person. Try two approaches in order. 1) see if you can tease out a discussion about the behavior without telling them someone complained about them. That move will always put them on the defensive (and perhaps permanently, potentially degrading relationships forever), and should be avoided unless absolutely necessary. 2) If you can't see any other way for them to recognize an issue they can work on, you may bring up that this behavior has been noticed by others. I don't see much point in naming names, unless you have to.
If there's been a blow-up...
If one or both parties engaged in overtly inappropriate behavior for which they need to apologize, I recommend you first go through the above steps, get agreement from both about a course of action, and then bring the parties together to mediate a solution and apologize.
I can't see many situations where you will want to do this, but not involve HR; this is their domain and you probably want to defer.
This step (the one you've been doing for so long) is kind of like a nuclear bomb. I wouldn't recommend it, because you are forcing a confrontation. There are a few potential outcomes:
- Both parties have already reconciled and you're dragging the issue through the mud again.
- Unlikely: Both parties are ready to reconcile and you will mediate a successful resolution.
- More likely: One or both parties are not ready to reconcile and you will at best get false buy-in to the resolution and at worst be mediating an actively volatile situation.
Workplaces are built on positive, constructive relationships and not by force. Therefore, "courts" or anything like them are unlikely to be a net win. They will exchange one problem for another.
Your best mediation will be to gently but firmly steer each person back towards desiring and actively working toward a positive relationship on their own.
In short, treat them like adults. Show them the benefits of harmony in the workplace. Show them the negative consequences of bad actions, if necessary. Let them figure out the correct behavior on their own. Avoid placing anyone in a defensive or uncomfortable situation.