I have that problem from time to time. For me, it is my left elbow. I think that it is a combination of things for me.

First, my saddle was no good for me and I was pitching too much weight on my hands to avoid saddle pain. I changed my saddle and now I can ride more balanced.

Second, I got some gloves.

Third, I am gaining more strength in my core and am more able to hold myself up in a good position without leaning too much on my hands and stressing my elbow.

Fourth, I may try a slightly shorter stem so i'm not reaching quite as far.

Fifth, I try to keep my shoulders at the same height so that I am riding more symmetrically and not putting more pressure on one side over the other.

I still get pain after about 20 miles or so, but it is less and less each ride so the things that I'm doing are working for me.