Whenever I try and make a pan sauce after cooking a steak I find I am adding almost a whole stick of butter before it even starts to thicken

In addition to the above responses, and assuming you're using stock in your pan sauce - the quality of your beef stock could also be a factor in thickening. If you're using homemade stock and the bones didn't have enough collagen (or the stock wasn't made well), the sauce could be difficult to reduce to the right consistency.

Or - if you're using store bought stock, try to find the kind that resembles soft jello at fridge temp (usually available at high quality butchers or specialty stores).

Sorry, I forgot about the shrimp: If you desire a creamier sauce, you can finish with a splash of heavy cream.

I think it depends on how you're making your sauce, so this might not answer your question at all, but I usually make it the same way I make turkey or chicken gravy: first make a butter and flour roux, add whatever stock you're using, bring it to a simmer and then add that to your roasting pan after you deglaze it with a bit of wine. This is just my made up methods but it's worked okay for me in the past. If you're making it a different way or not using stock you can ignore this answer! Usually I don't have enough drippings to make a sauce without adding more liquid to it.

Often times you'll read about using butter to "thicken" a pan sauce. Chef June uses a much better term above. Also, the butter should be very cold, you want to "mount" it off heat, and serve immediately. Properly done, the butter remains emulsified after it melts into the sauce. There is a little thickening but it's more about mouthfeel and taste.

It's really hard to know what's happening without knowing what other ingredients you are using to make the sauce. If you are deglazing the pan with a liquid (picking up all the lovely brown bits and fond that have developed in the pan while cooking the meat), and then you cook that resulting liquid down to nearly a syrup, you should need only a "chunk" of butter to "silken" the sauce.

How are you making your pan sauce?

Instead of just butter, use beurre manie which is mixture of equal parts flour and butter. You'll probably need to deglaze the pan with a little liquid, but swirl in the beurre manie. It should thicken your sauce up.