Ceramics don't normally go bad but if they do I assume they go short circuit as the dielectric has been damaged. I suppose it's possible for them to go open circuit but the only way I can see it happening is if it's been mechanically damaged, i.e. the ceramic is chipped and the wires are starting to come loose.
Nigel would disagree but I've never seen any tantalums go bad but according to him they fail short circuit which makes things easy.
I would check both ceramics and tants on a multimeter with the resistance setting, they should read open circuit, then with the capcitance setting, they should be within their rated value by about 20%.
If your meter doesn't have a capacitance setting then you can make your own very basic capcitance meter with an astable multivibrator like the 555 timer.
