However this particular term is used when two opposing gendered heterosexual individuals engage in conversation and something is said that could be perceived in a way other than intended. Just as "nohomo" implies there is no homosexual connotation to the aforementioned statement, the term "noromance" implies that there is no romantic implications intended in the response or statement of either heterosexual opposite gender individual.
Generally this is only used by men who are in a loving, committed relationship when talking to old acquaintances or networking, or women who want to keep guys in the friendzone.
Platonic Male: So the other day, I made the mistake of asking my friend, who happens to be a wizard who takes everything literally, to make me a sandwich. I was delicious.
Platonic Female: OMG LOL You're sooo funny! I love you haha
Platonic Male: I love you too noromance!
Male Pursuing Female: Hey my friends having a party later you should come by, there is going to be punch and pie.