The problem with simply trying to align two tables next to each other is the variable browser behaviour. The majority of browsers will, if the total width of your tables is even close to 100% of the window width, split them onto two separate lines.
Therefore, the easy fix is to nest those tables within another table.
Code:
<table><tr><td>
<table><tr><td>This is your first table</td></tr></table>
</td><td>
<table><tr><td>This is your second table</td></tr></table>
</td></tr></table>
Then, if you want the tops of the tables to align with each other, then you simply add "valign='top'" to your outer tr tag. If you want the middles of the tables to align, you valign the row to middle, etc.