In order for a constitutional amendment to be sent to the states, a 2/3 vote of those present (subject to a quorum) must vote for the bill. This is not spelled out in the Constitution but rather in either the legislation speaking of the bill or if silent on the matter, the rules of each chamber. If a serious amendment were to be adversely affected by this, you can be sure there would be a rule clarification.
The more interesting question comes when you count the 3/4 of the states that need to ratify it. Two amendments in particular have raised questions.
First, the 27th Amendment initially only needed 10 states to ratify it- but it languished so long that for years it just sat. Over the years many states ratified the "no congressional pay raise without an election amendment" as a protest, but when Michigan passed it in 1992, it became the 38th state to do so.
On the flip side, there is a common misconception about the Titles Of Nobility amendment that has many people thinking that it should have been the 13th amendment to the Constitution. There are stories that Virginia passed it in 1816, but the fact was not communicated before additional states were added to the Union, unfairly leaving it out. In fact, the amendment was never that close to being ratified, but it proves the point that the amendment must pass 2/3 of the Congress and 3/4 of the states at the time of ratification.
This link talks about the Titles of Nobility Amendment, the 27th Amendment, and ratification quorums.