Convert vga to HDMI
Solution 1:
It is possible, but not trivial. You will need an actual active converter rather than a cheap cable. The reason for this is that HDMI is digital only, and the old VGA signal is analog.
As to the quality, that depends on the output on your VGA/DB15 plug and on the quality of the convertor. I looked before and I could not find any limitation in the VGA standard. However most VGA cards come woth a 400MHz DAC which would commonly limit it to any configuration using a lower than 400MHz bandwidth. (E.g. 2048x1536@85Hz which needs 388 MHz bandwidth). If your DAC is less capable or there are other limits then the maximum resolution will be lower.