What happens when a male with an x linked recessive genetic disorder has children with a female who does not carry the disease?

No disease, but...: The scenario you describe would result in a male infant being totally normal, while a female infant would be a carrier that would most likely be unaffected, given that the mutation is recessive. Depending on the actual disease, it is theoretically possible for the female infant to have mild symptoms, since one x chromosome in each cell gets randomly shut down (lyonization).