Wattmeter Required for Transfomer Characterization?
I do not have a wattmeter, but I do have two multimeters. Wherever a
  wattage is required, I can just measure the Amps and multiply it with
  the Voltage, right?


No, that doesn't work in AC circuits when the impedances are reactive/complex.

There is a thing called "power factor" - this relates actual power to the RMS values of current and voltage. If you have a pure inductor supplied with an AC voltage and AC current will flow. This does not mean that a power is produced by the inductor of \$V_{RMS}\cdot I_{RMS}\$.

Because, for a pure reactive component current and voltage are displaced by 90 degrees, the theoretical power is zero.