STK includes a powerful calculation for computing conjunctions with Space objects from known (or unknown) missile trajectories.
A known trajectory can be applied as well as a time span around that trajectory along with uncertainties in the launch and impact locations. All of these are then rapidly computed against a satellite database to identify clear-firing or blackout windows.
Please reference the STK Help on Using the Launch Window Analysis Tool
for more information.
Here is a video showing it in action: