Is narrow-band ultraviolet B (nbUVB) phototherapy contraindicated or recommended with caution in patients with a personal history of melanoma?  

Although it is challenging to be definitive, our current literature suggests that nbUVB does not increase the risk of melanoma or nonmelanoma skin cancer.Previous studies suggesting a possible increased risk with nbUVB included patients with a history of PUVA, which has been shown to increase risk. ...

I agree that it can definitely be considered when needed. But you should consider other options first. It is definitely much safer than PUVA.

I agree with Dr. @Nicholas that the literature is reassuring. I often cite this literature when I would like to reassure someone that it is safe to do pursue NBUVB. When confronted with patients who have a history of or new diagnosis of melanoma in addition to inflammatory disorders like psoriasis ...

Quite the irony, quite the enigma. With rare exception, Narrowband UVB appears to be safe for use in so many who have a history of skin cancer but the biggest obstacle to its use appears to be the US.