Self-empathy seems to me to be a form of luminosity.

Since you're with yourself all of the time, I'd say it is useful pretty much all the time.

Edit: Wow, this was timely. Barking up the wrong tree just posted this:

Study after study shows that self-criticism is consistently associated with less motivation and worse self-control. It is also one of the single biggest predictors of depression, which drains both “I will” power and “I want” power. In contrast, self-compassion— being supportive and kind to yourself, especially in the face of stress and failure— is associated with more motivation and better self-control.

As a practical matter Theater has been shown to increase empathy for those on the Autism spectrum (hi!) so if you consider yourself particularly bad at empathy (also hi!) then I would personally recommend theater and improv.

http://www.sensetheatre.com/pdf/researcharticle.pdf

Maybe there are tips to be found here : http://lesswrong.com/lw/6tb/developing_empathy/

Compassion meditation is one way. Check out the methods section of this article for a description of the meditation and the pictures to see how the brain looks during meditation and the conclusion to hear about how this type of meditation effects the areas of the brain responsible for detecting emotion in oneself and others and understanding other's mindsets.