What resolution can the eeePC 1001HA/1101HA handle with an external monitor plugged in?

I own an Assus EEE901 and a EEE Box, both are able to drive my 24" (1900x1200) monitor.
I would assume both laptops you mention can do the same.

On 1101HA 1920x1200 (WUXGA) works without problems.

1001HA is reported to do at least 1920x1440. According Intel's specs GMA 950 (found in 1001HA) is capable of 2048x2536 maximum resolution but I would be surprised to find such a resolution to work with netbooks.

And as Asus's netbooks have D-Sub instead of DVI adapter, the resulting image quality can be rather poor with large resolutions.