Crystalline armor has the highest damage level of all armors. If the damage from the mines is not enough to actually destroy the armor, it will still be there even though the mines did explode.
There was a bug noticed with mines and colony ships, btw. The colony component is so huge that a single mine of any tech level cannot destroy it and so a colony ship would be an effective mine sweeper that could clear an entire minefield by itself (although everything but the colony component would be destroyed...) This was because each mine attack was counted as a seperate combat. If this has not been fixed, then crystalline armor will be very good protection against mines that do less than whatever damage level your armor has. Organic armor, too.