Atomic Clock
I think that a highly likely possibility has been missed. There is a very good chance that you will land on a planet with a high level of technology. If there is a working timegate then this is almost certain.
Answer
Any technologically advanced society will know the speed of light and have atomic clocks. These will work at the same rate anywhere in the universe. Provided the traveller knows the speed of light then everything else can be translated into local time units. Even if the technology is only at 19th century Earth level, our traveller can talk to their scientists and pass on the necessary information to make a measurement of a suitable constant. They will be grateful that their science has been boosted and will be predisposed to help him return.
EDIT
People seem to be shooting first and asking questions afterwards. Or rather, in this case, they are raising an objection but down-voting before waiting for an answer. The assumption seems to be, "I know better therefore there can be no valid answer to my objection." When I have a minute I'll do some actual calculations and show how the calculation would be done and the amount of error that can be expected.