The solution to this problem is using the table-cell display properly and avoid the floating:
<div id="OptionsPanel">
<div style=" width:300px; display:table-cell; vertical-align: middle; background-color:Blue; ">
<div style=" display:inline-block;">
<img src="Media/1/M113906234611W.jpg" id="ctl06_MediaImage" alt="Option 1" />
</div>
</div>
<div style=" width:300px; display:table-cell; vertical-align: middle; background-color:Blue; ">
<div style=" display:inline-block;">
<img src="Media/1/M113906234612W.jpg" id="ctl07_MediaImage" alt="Option 2" />
</div>
</div>
</div>
My error was thinking that a clear would make floating divs as tall as their parent.
Using table-cells makes them automatically as tall as the parent div. height:100% or min-height: 100% doesn't work normally.