Learning to estimate for my team was an initial challenge for me expanding into a management role as well. I was the most experienced member and would estimate for my speed, but others would fail to meet those dates.
I'm in agreement with Emil Moe, you need to break it down into the smallest tasks then estimate those. You will have to spend some time learning weaknesses of you team members and their individual speeds, OR you can include them in the quoting process.
One team found success by sitting together for an hour twice a week to review tasks and estimate together. Business would approach the manager, the manager would begin to break it into tasks and clean up the spec for the developers, then he would have it prepared for the next team estimation session. They could quickly quote small tasks so the process was relatively fast.
This method also puts more brains on the spec, it can help identify gaps or conflicts in logic that business missed. These gaps/conflicts are the worst surprises that impact my deadlines.