If certain employees fight in the middle of a very significant meeting, would you continue with the meeting or stop it?

It is a failure of my management skills if I let them fight and also failure of healthy organizational culture also if people are rival to each other . I will stop the meeting for a while and try to identify the core issue . Also I will figure out the best solution to make them work as a team . Meetings means discussion of important issue , so it will continue after a short brake .

I openly encourage debate in all my meetings. What is a fight for someone is robust discussions for others. If the meeting is internal, i would council people involved if it became personal, maybe issue a yellow card eg some time out. If it doesnt improve then potentially a red card, ejected from meeting. If it is a meeting with external parties that involves serious negotiations this sorting of thing is the worst thing that can happen. You need to ensure you and your team are in agreement to mitigate the risk of conflict. if the meeting is disrupted by "fighting" i would call time out and deal with it and not lose any bargaining position with my opponent. 

I would remove them from the meeting and continue normally. After the meeting, I would talk to them and try to figure out what happend, so I could take the correct actions.

What kind of fight are we talking about? words or fists? because while it might sound strange the latter can also take place. What you need to do is ensure that everyone feels that their ideas are heard and appreciated, you must strike a balance between the people present in the meeting so no one feels that they are wasting their time as you are interested in only one person who you like to hear. Make sure everyone gets a chance to express their ideas but at the same time let it be known that uncouth and unprofessional behavior will not be targeted. Be the mediator rather than become the spectator. Also if you feel that things are getting heated step in immediately because if you do not, after the end of the meeting, you would have two people who are angry with each other and that anger will ultimately affect your business in some way down the line.

Depends... if you are chairman of the meeting you stop the meeting, if you are participant be tactful and do not support the fight. 

Typically before every meeting we have set agenda, and may ask for the suggestions before hand for all significant meetings. Still if there is an instant friction that may crop-up between team members, in that case I will put hold on the topic that is creating friction and continue with the meeting . Regarding the conflicting issue I will sit with the team members separately and try to resolve it amicably.      

A good team leader will ask both of them to leave the meeting room and meet them separately to clear the misunderstanding or difference in opinion. No one should be allowed to spread nuisance in meeting room. Meeting room is the area where we should celebrate acheivement, discuss process & product, difficulty in selling product, etc.

I would like not to use the word argument. Instead, I would like to keep it as a 'discussion'. However, it needs to be critical and with rationale or evidence. Otherwise, these discussions will turn out to eventually reflect in the work culture. 

I would diligently interfere and try to navigate the direction of conversation (argument) to a meet the objective of the meeting. Another effective way is the indirect way of saying stop to the argument, by introducing another subject (relevant).

Definitely I will stop the meeting and I will listen to both sides and at the end will figure it out what is the best solution to the situation/problem.

I would pause the meeting first, attend to the employees who are fighting and try to solve the problem peacefully. After the employees have calmed down we would resume the meeting.

If a fight happens in a meeting. I will pause the meeting for sometime. Once the fight is over. Or once we come to a conclusion of the fight. Meeting resumes.