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Depending on the size of the stuff you want to keep in the pan and the time-criticality:

- Strainer.  You mentioned that your pasta strainer's holes are too big.  I have colanders with holes of two different sizes, a larger conventional one and a smaller one with smaller holes.  (I use the latter to strain small vegetables like corn sometimes.)

- Strainer + cheesecloth.  If your strainer's holes are too big, line the strainer with cheesecloth and then strain.  This will be slow and it won't work with a thickened broth, but if your broth is mostly water it should work.  Where I live, cheesecloth can be found in the grocery store either with the foil/plastic wrap/parchment paper/etc or in the baking aisle.

- Lid.  Hold the pan over the sink (or receptacle, if you want to keep the broth), hold the lid over and at an angle from the pan to create a narrow channel, and pour.  This takes a little practice, so do it over a bowl the first time so if you let too much stuff through you can recover.

- Baster.  This is the slow way, but a baster is a tube with a small opening on one end and something you squeeze on the other end to create vacuum.  You can use this to remove liquid one baster-full at a time.  (Its normal application is to suck up liquid and pour it back over what's in the pan, hence the name.)  Using a ladle would be faster, but I assume you're not doing that because you're getting too much stuff you don't want to remove.