One of the petitions was filed by senators led by Gen Somjate Boonthanom and the other by senators led by Sai Kangkavekin.
The court said it dismissed the petitions because there was no reason to act as requested.
The constitutional amendment was sent to His Majesty for approval through the Office of His Majesty's Principal Private Secretary on Tuesday after it was signed by Prime Minister Yingluck Shinawatra.
Ms Yingluck said before the court's ruling that she was duty-bound to forward it and insisted that it was drafted in accordance with the process stated in the charter.
The court also considered a petition filed by 50 senators led by Paiboon Nititawan and 62 Democrat MPs led by Wirat Kallayasiri for it to rule whether the 2014 Budget Bill's Section 27 regarding reduced allocations for the Office of the Judiciary and Office of the Administrative Court and Section 28 in the budget for the National Anti-Corruption Commission (NACC) violated the constitution.
PM's Office Minister Varathep Rattanakorn, deputy chairman of the parliament's budget bill scrutiny committee, and representatives of the Office of the Judiciary, the Office of the Administrative Court and the NACC as well as a representative of the Budget Bureau, were summoned to testify to the court on Wednesday.
After hearing their testimony, the court said it would make an oral statement and a ruling on the petition on Friday.
The court also agreed to accept a revised petition filed by Democrat MPs led by Pirapan Salirathavibhaga for consideration.
The petition asks the court to rule whether the draft amendment to the constitution concerning the composition of the Senate violates Section 68 of the constitution.
Mr Pirapan and the Democrat Party's legal team submitted to the charter court a video clip of a government MP allegedly logging in to vote on behalf of absent lawmakers during the joint parliamentary sessions on charter change on the make-up of the senate on Sept 10-11.
The clip was presented by the opposition party as evidence for the court to consider.
The first version of the petition asks the court to take action against those appearing in the clip, but a revised petition includes all lawmakers voting for the bill, and others involved.