Latest results from the BASE experiment at CERN published in Nature  shows that the charge-to-mass ratios of protons and antiprotons are the same to a precision of 16 parts per trillion. This is a new record in precision.
(charge_proton/mass_proton) / (charge_antiproton/mass_antiproton) = 1.000000000003(16)
This high-precision measurement was achieved by comparing the cyclotron frequencies of antiprotons and negatively charged hydrogen ions (negatively charged proxies for protons) in a Penning trap.
The result is consistent with charge–parity–time-reversal (CPT) invariance, which is one of the cornerstones of the Standard Model of particle physics.
On the question of whether the antimatter (antiproton) obeys the WEP (Weak Equivalence Principle) the answer from the BASE experiment is “yes”. They quantify their answer with a limit (see the abstract below).
There is another experiment at CERN called ALPHA which makes similar measurements. It will be interesting to compare the results from ALPHA and BASE.
“The standard model of particle physics is both incredibly successful and glaringly incomplete. Among the questions left open is the striking imbalance of matter and antimatter in the observable universe, which inspires experiments to compare the fundamental properties of matter/antimatter conjugates with high precision. Our experiments deal with direct investigations of the fundamental properties of protons and antiprotons, performing spectroscopy in advanced cryogenic Penning trap systems. For instance, we previously compared the proton/antiproton magnetic moments with 1.5 parts per billion fractional precision, which improved upon previous best measurements by a factor of greater than 3,000. Here we report on a new comparison of the proton/antiproton charge-to-mass ratios with a fractional uncertainty of 16 parts per trillion. Our result is based on the combination of four independent long-term studies, recorded in a total time span of 1.5 years. We use different measurement methods and experimental set-ups incorporating different systematic effects. The final result, (q/m)proton/(q/m)antiproton=1.000000000003(16), is consistent with the fundamental charge–parity–time reversal invariance, and improves the precision of our previous best measurement by a factor of 4.3. The measurement tests the standard model at an energy scale of 1.96 × 10−27 gigaelectronvolts (confidence level 0.68), and improves ten coefficients of the standard model extension. Our cyclotron clock study also constrains hypothetical interactions mediating violations of the clock weak equivalence principle (WEP_cc) for antimatter to less than 1.8 × 10−7, and enables the first differential test of the WEP_cc using antiprotons. From this interpretation we constrain the differential WEP_cc-violating coefficient to less than 0.030.”