"Here is my two cents" vs "Here are my two cents"?

Solution 1:

I'd posit that the "here's..." version is preferable, on various grounds.

As the OP suggests, the implied meaning is "here's my two cents worth". In fact this idiom is likely derived from (or at least cognate to) the common British English expression:

Here's my tuppenceworth

(Tuppence = 'two pennies'). https://en.wiktionary.org/wiki/tuppence_worth#English https://books.google.com/ngrams/graph?content=tuppenceworth&year_start=1800&year_end=2000&corpus=15&smoothing=3&share=&direct_url=t1%3B%2Ctuppenceworth%3B%2Cc0#t1%3B%2Ctuppenceworth%3B%2Cc0

Also "my two cents" is clearly a singular thing in this idiom (meaning 'my opinion'). By using is, rather than are, you avoid any ambiguity: it's clear that you're not referring to two individual 1c coins.

And - just from my own experience - I've heard variations on the "two cents" and the "tuppence" phrases many times, and it's always been with the is form. "That's my two cents" sounds fine, "Those are my two cents" sounds very awkward, archaic and pedantic.

To sum up: yes, the standard laws of grammar would require the verb to agree in number with the object (in it's literal sense), but with a common idiom like this, conventional usage defines the grammaticality.

Solution 2:

Here's my two cents on the subject.

Interestingly the ngram viewer doesn't find a single occurrence of are my two cents. The actual book search does however. Guess those books are not part of the corpus ngram is based on.

However there is a clear rising trend of 's my two cents (top four of all phrases ending in my two cents) and here's my two cents. (Ngram)

Of course the Google Ngram Viewer is not an explanation regarding why that singular version is highly preferred and the usage of is and it's contraction is on such a rise.

As you have already written in your question it's short for two cents' worth (ODO) and as such the singular usage would be logical.