EDIT:
Having written a long reply it strikes me that you may be doing this in an unconventional way. The HTML of the page should be in the .aspx not in the code behind (.aspx.cs).. it isn't impossible to put it in the .cs file, but "normally" the HTML would be in the .aspx. Why? Because of exactly the problem you describe, it is painful to maintain!! Normally we would separate the C# code from the HTML...
In your example, you are not dealing with the quotation marks correctly. " should become \"
Consider
myString+= "<div class=" + "clear" + "></div>";
should probably be
myString+= "<div class=\"clear\"></div>";
You could also consider these options, depending on what you are trying to achieve one of the following should help you
1 String literals
If you want to add a string "exactly" as it was given, you could use the string literals. All you do is stick a @ when you declare the string. (http://www.dotnetperls.com/string-literal).
You will also need to escape your ", by using ""
For example:
string longstring = @"<h3>Hello</h3><p>Name<sup>®</sup> some text<div class=""clear""></div>";
string longerstring = @"<p>String literals are stored in the metadata format that underlies
all executable C# programs. The metadata format defined in the Common Language
Specification includes a database of tables with headers and rows in all exe
files. There are several predefined streams in the metadata files, including the
#Strings stream and the #US (user strings) stream. The #US stream is used to store
programmer-defined literals. The metadata tables store offsets into this stream.
The stream itself is simply a concatenated series of characters used in the entire
program's strings. The execution engine stores the offsets and tables in memory
and then simply reads a range in the #US stream when you use the string literal.</p>"
2 Resources
But if you are only storing static parts of the page, ie HTML snippets you could use .resx resources (http://msdn.microsoft.com/en-us/library/ekyft91f(v=vs.80).aspx) ... OR
3 Server Side Includes
possibly even server side includes
<html>
<body>
<%
Response.WriteFile ("Yourfile.inc")
%>
</body>
</html>
Where Yourfile.inc is a file on your file system
http://support.microsoft.com/kb/306575