The combination mw became nw in (Ancient?) Quenya, a sound change mentioned in the Outline of Phonology (OP2) from the 1950s:

mw became dissimilated > nw (OP2: PE19/97).

In a marginal note Tolkien also considered mw > mm (PE19/97 note #141) but the one late example of this sound change shows nw as a result:

• ✶sam-wē > Q. sanwe “thought” (PE17/183).

In notes discussing Eldarin comparison from the mid-1960s, Tolkien said “mw later dissimilated to nw” (PE17/92), affirming that this was the normal phonetic development.

Conceptual Development: There are examples of mw > nw appearing in the Qenya Lexicon from the 1910s:

• ᴱ√AM(U) > ᴱQ. anwa “high up” (QL/30).
• ᴱ√KAMA² > ᴱQ. kanwa “dark red” (QL/44).
• ᴱ√RAMA > ᴱQ. †ranwe “shout” (QL/78).

However, in the Outline of Phonetic Development (OP1) from the 1940s Tolkien said:

mw was avoided, or became prehistorically mm (OP1: PE19/47).

There is one clear example of this sound change in The Etymologies from the 1930s:

• ᴹ✶hamwa > ᴹQ. hamma “chair” (EtyAC/KHAM).

In the first versions of this entry Tolkien seems to have given the Noldorin cognate of this word as hanw (its exact form is hard to read); in the rewritten entry he gave both ham and hanw as alternate cognates (EtyAC/KHAM). The Noldorin word hanw seems to indicate that the change mw > mm was Quenya-only, but ham probably means the sound change occurred in Primitive Elvish, affecting both branches of the Eldarin languages equally.

As indicated by the marginal note described above, Tolkien seems to still be considering mw > mm in OP2, but by the 1960s it seems the development was exclusively mw > nw. If so, the conceptual development of this sound change would be: (1910s) mw > nw, (1930s) mw > mm, (1950s) mw > nw. There were similar vacillations on the development of mw in Sindarin.

Hat tip to Lokyt for telling me about the mid-1930s rule from OP1 and the quote from PE17/92 which gives a much clearer picture of the conceptual development.