I am new to freelancing work, currently have no client and been in touch with two clients who show interests on my service. We met couple times already but both client seems not moving the process to discuss the contract detail, I just afraid if I ping them too often that will cause backfire, how exactly should I handle in such a sticky situation?
There are 3 levels of 'Yes' in negotiations.
Yes - just to get the discussion going.
Yes - agreement with what you are saying.
Yes - commitment level 'yes' backed with action.
If you have sent in your estimates, details, etc., as @Scott mentioned above, and there's no response yet in terms of making payments, move on like you never met them. Go and find more clients.
Serious clients pay to kickoff their projects. Otherwise, they are just prospects.
I hope this helps.
Since you're new to freelancing, I'd add that getting clients to commit often takes a surprising amount of time - even when the meeting(s) have seemed nothing but positive.
There is very little one can do to speed up the process, as one never knows the reason for the client dragging their feet. It could be complicated internal processes or lack of processes or just downright human laziness.
As stated in the other answers, generally the best option is making the client feel you are a sought-after commodity that would like to work for them, but otherwise has other stuff to do.
I haven't ever been able to fast-track a client's decision making, but I have seen others attempting to lure a client by 'reserving' some time in the near future which would be dedicated to them, if they commit now. While this may work, my general impression aligns with that of @Scott, that having made your pitch, your work is done.
They are interested when they sign a contract with all the important details of the project. I might contact them once or twice via email to follow up, since that's easy, but often things change, budgets change, management changes their mind and they go with another vendor or the project just gets dropped. Don't take it personally. This is part of business.
I provide estimates, details, etc.
Wait a week.
If I hear nothing, I'll reach out once. Asking if they have any further questions I can assist with. Often a client may tell me at that time that they've decided to go a different direction. But if they don't....
I pay them no heed until they contact me.
If they never do, then they decided against hiring me. My time is far too valuable to be hunting people down. If they are interested, they'll be in touch. In addition, appearing too eager can come across as too desperate -- leaving you open for poor negotiations or simply not getting work because you seem too "needy".