"承诺" is a verb, promise to do something, "诺言" is a noun, means words that people said when they promise

1your+承诺，承诺+you do something 2your+诺言

承諾=promise now 諾言=The thing you already promised 我承諾我可以做到 I promise I can do it 我會記住你的諾言 I will remember what you promised Sometimes you want to punish that person forgot him/her promise 你忘了你曾經承諾過我什麼嗎？ / 你忘了你對我的諾言嗎？You forgot what you promised me?

承诺和诺言都可以作名词，意义无明显差别(no obvious difference)。我们常说： 实现/遵守/许下/记得+承诺/诺言 eg. 你要记得你曾经许下的诺言/承诺。You must remember the promise you made before. 不同：承诺还可以作动词，诺言不可以。 我承诺过老师一定要学好汉语。（T） I promised my teacher I would study Chinese well. 我诺言过老师一定要学好汉语。(F)

"承诺": the emphasis lies in 承 and 诺, which respectively mean "to admit/take on" and "to make a promise", both characters are verbs. The phrase composed of two characters with similar meanings means the similar to each of the separate character. This is rule that applies to many other Chinese phrases, such as 放弃，阅读，观赏，吟诵, etc. "诺言" : the emphasis lies in 言, a noun, "word", what word? the word of promise=a promise.