From having done this in a house of the same vintage, two practical notes.
Do not connect the ground terminal to the neutral to make a tester show a ground. This is occasionally suggested and it is genuinely dangerous — it puts normal return current on the appliance case and makes an open neutral lethal. Any tester showing a proper ground where none exists is worse than one showing the truth.
A plug-in tester will report a fault on these outlets and that is expected. Those testers detect the missing ground and cannot detect a working interrupter without a ground. Use the test button on the device itself, monthly.
Also worth knowing that in some cases running a single ground conductor back to the panel for one circuit is permitted and is far less work than rewiring. Worth asking about for the circuits that feed your electronics.