Friedrich Nietzsche wrote on promise-keeping in Genealogy of Morals as a result of a refined, and thus cultivated “breeding” of our species, rather than as an innate part of human nature that can be taken out for a spin on day one. In contrast, lying is more expedient and thus primitive in our nature, as if an instinctual urge that is more reflex than refined. In terms of romantic relationships, whether marital or not, “cheating” sexually is definitely a sign of weakness because it places momentary pleasure above being held as reliable (i.e., trustworthy) in terms of promise-keeping. A boyfriend who admits that he might hurt his girlfriend emotionally by engaging in infidelity is really telling her that he is weak-willed and thus not good boyfriend (or husband) material. To be sure, a couple could agree that both can have sex separately with other people, so not being monogamous need not involve violating a promise. I don’t think Nietzsche’s philosophy goes so far as to embrace such an arrangement (especially if romantic feeling or connection is allowed in the separate sex), but neither is monogamy advocated, given the nature of Nietzschean strength that should be allowed out of the cage of societal convention periodically (but not on a regular basis). The concept of strength plays such a powerful role in Nietzsche’s philosophy that even the occasional raw expressiveness of strength beyond a societal straitjacket of moral convention would not be viewed as violating promised monogamy. I have a friend who periodically spends thousands of dollars to travel to and attend Mariah Carey concerts. Even though he parties at them, he told me that he has not been unfaithful at them. Nietzsche would chastise my friend’s sense of moral obligation and say that the innate, human strength of will and power in embracing living to its resplendent fullness without shame needs (and deserves) occasional stints of breathing room, similar to how ancient Roman conquerors occasionally were able to pillage villages and even seduce or even rape beautiful captured women. To Nietzsche, this does not count as infidelity, given the nature of the strong; not even the wives of the Roman conquerors would have considered their husbands to be breaking their marital vow of sexual fidelity. In utter contrast are the weak-willed, who shamelessly manipulate and lie even to such a person whose love is genuine as if weakness itself requires constant sex with other people—even with other “partners.”
The full essay is at "Nietzsche on Promise-Keeping."