It certainly looks like amber. The discoid inclusions are very typical, as are the various organic material within.
Besides observation under magnification, two tests that are typically performed are specific gravity and a hot point. Specific gravity requires a loose gem, so that's basically out.
To perform a hot point test, heat up a needle with a flame and immediately put the point on an inconspicuous spot on the gem. Amber will have a pleasing pine like aroma, where an imitation will produce an acrid burnt plastic smell.
Three things to consider with the hot point test are 1) be careful; 2) this is a destructive test, so use judiciously; and 3) it does not identify reconstituted amber, which is always also a possibility.
With this and your other agate piece, remember that amber is very light, and chalcedony has more heft to it; you can get a good feel for amber just on how light it is in your hands. Also, if you tap two pieces of the gems together or tap them with your fingernail, chalcedony "clicks" like glass and amber "clacks" like plastic.
Good luck!
