The convention, mentioned by Cerberus (CHAT): "The first accusative is taken as the primary argument of the infinitive, if there is ambiguity (i.e. no context)." is also given in my elementary text (Oulton) when translating an accusative and infinitive.
"iudex sciebat servum militem interfecisse." =
(a) "The judge knew that the soldier killed the slave."; or:
(b) "The judge knew that the slave killed the soldier."
By convention the answer is (b).
Similarly, it can sometimes be difficult to tell which infinitive to take as part of the accusative and infinitive e.g.
"legatus nuntiavit hostes pacem accipere velle." =
(c) "The ambassador told the enemy that he wants to accept peace."; or:
(d) "The ambassador told the enemy that he accepts that they want peace."
Having accepted that "hostes" must be the subject of the indirect statement, then which infinitve?
By convention the answer should be (d); but, this is coloured by the grammatical reality that verbs such as "volo", "nolo" & "possum" generally govern an infinitive e.g. "He wants to do/ to run/ to read."
By this "convention" the answer would be (c).
Without context use the convention and hope that the writer has done likewise.
Returning to your example: "puto eam me amare."; by convention = "I think she loves me."
To reverse this: "puto me eam amare"; by convention = "I think I love her."
If you are the writer than try the examples in Seb's, Joonas's & cnread's excellent answers, in the original Q., which obviate the need for approach-by-convention.