Sprinkle some cayenne pepper into a mixture of about 2 tbsp lemon juice and 2 tbsp honey - microwave for about 20 seconds and then stir. Drink it while it's hot.
It doesn't necessarily "cure" my sore throats, but it always makes it feel better. I get tonsillitis that seems to be triggered by my sinus problems and constant post-nasal drip. The cayenne pepper always helps me cough up all the nastiness back there.
If you like pickle juice (I love it), I have also found it helps to drink a couple sips of it mixed with cayenne pepper. This doesn't soothe my throat like the honey/lemon, but it does help me cough up excess mucus.
I tried the lemon and honey trick, with about 1/8 teaspoon of cayenne, microwaved it for 20 sec, then tried to gargle it and burned my tongue and bottom of my mouth badly. Make sure it's not too hot, or it will just make it worse.
Cayenne Tips
I tried the 3 tbsps of honey with 3 tbsps of lime juice, since I didn't have lemon juice on hand. I generously sprinkled cayenne pepper and added a few drops of water. Heated it 20-30 seconds and drank. I tasted pretty good and I could immediately tell that in was "working" on the sore areas of my throat. I immediately got my voice back and am very hopeful that this will give me relief throughout the course of this sore throat. I will repeat as necessary until the sore throat is gone. I speculate that it doesn't cure the sore throat, but numbs it. But that is good enough for me. With the symptoms reduced, I can certainly wait this thing out!
Apple Cider Vinegar, Honey

when I have a cold or a sore throat or I lose my voice I take a tblspoon of honey and apple cider vinegar... works like a charm! The after taste may burn a little bit but not bad.
Cayenne Tips
You must know something about honey. It is extremely healthy, but loses it all if you heat it to the temperature higher than 40 C (103 F). After that you have only sugar, which is harmful. So: STOP NUKING YOUR FOOD!