The best response is to show no embarrassment yourself. A direct, matter-of-fact attitude helps the person save face and helps you both deal with the situation rather than focusing on
the feelings around it.
That's not to say you should ignore the feelings. Simply acknowledge them with empathy and move on: "I see you wet yourself. It happens, sometimes. In fact, it happens to a lot of people when their bladder starts to work differently. Not a big deal -- here, let me help you." Or for repeated accidents: "Oh, Mom, I know you're frustrated. You've been having a lot of problems. Would you like to go to the doctor to see if there's some medicine or something that can help?"
If humor is a style that works for you both, this can be a good opportunity to use a little of it: "Well, I guess now you can be like those glamorous ladies on the TV commercials who are advertising all those protection products!"
What if you can't help it -- you are embarrassed? Don't try to hide it. Admit it (but do so with sensitivity): "Well, I'm not sure what to say. I know you don't like me talking to you about something so private." Many older people are very good at tuning in to your real feelings and appreciate your being direct about them.