After the call to CreateConnection, call the Open method on workflowManagementServer.Connection.

Check out the Developer Reference for several examples on creating and using connection strings.

Thanks for the response.

 I got the same results when I used workflowManagementServer.Connection.Open versus workflowManagementServer.Open.  It still threw the ConnectionString exception.

 However, your tip about looking in the Developer Reference seems to help.  Rather than just passing my long connection string, I used the method from the Developer Reference.  So i'm guessing there was just something wrong with my connection string.  Even though the information in my string seems to be the same info I'm building here, there was probably something wrong.  Following is the code that I used from the Developer Reference to create the connection string in case anybody cares.  Thanks again for the help.

SourceCode.Hosting.Client.BaseAPI.SCConnectionStringBuilder connectionString = new              SourceCode.Hosting.Client.BaseAPI.SCConnectionStringBuilder();

connectionString.Authenticate = true;            connectionString.Host = K2Server;

connectionString.Integrated = true;            connectionString.IsPrimaryLogin = true;

connectionString.Port = K2Port;

WorkflowManagementServer workflowServer = new WorkflowManagementServer();

workflowServer.CreateConnection();

workflowServer.Connection.Open(connectionString.ToString());

Sorry, the code I just posted is formatted poorly.  Basically, using the SCConnectionStringBuilder class seemed to fix the issue.

Ooops, I still get the connection string error.  I've tried to narrow things down as much as possible.  I have 2 methods to get the connection, but either way I get this error as soon as I call the ZonCalculateEvent function.  Does anybody have any more ideas?  Here is my code:

//method 1 to create and open connection

WorkflowManagementServer workflowManagementServer =

workflowManagementServer.Connection = workflowManagementServer.CreateConnection();

SourceCode.Hosting.Client.BaseAPI.SCConnectionStringBuilder connectionObject

=

connectionObject.Authenticate =

connectionObject.Host =

connectionObject.Integrated =

connectionObject.IsPrimaryLogin =

connectionObject.Port = 5555;

workflowManagementServer.Connection.Open(connectionObject.ToString());

workflowManagementServer =

workflowManagementServer.Connection = workflowManagementServer.CreateConnection();

workflowManagementServer.Open();

Hi Dave,

The error message is a bit misleading, but you are basically missing the zone from which you want to get the due date. So add the following line before calling the ZoneCalculateEvent and it should work:

wfManagementServer.ZoneLoad("My Zone");

The following worked for me:
WorkflowManagementServer wfManagementServer = new WorkflowManagementServer();

wfManagementServer.CreateConnection();

SourceCode.Hosting.Client.BaseAPI.SCConnectionStringBuilder connectionObject = new SourceCode.Hosting.Client.BaseAPI.SCConnectionStringBuilder();

connectionObject.Host = "blackpearl";
connectionObject.Integrated = true;
connectionObject.IsPrimaryLogin = true;
connectionObject.Port = 5555;

wfManagementServer.Connection.Open(connectionObject.ConnectionString);

TimeSpan tSpan = new TimeSpan(0, 10, 0);
wfManagementServer.ZoneLoad("My Zone");
DateTime dueDate = wfManagementServer.ZoneCalculateEvent(DateTime.Now, tSpan);

I've done some testing now and it seems that you have to call 

workflowServer.ZoneLoad("Standard");

before ZoneCalculateEvent, otherwise this error occurs the first time the K2 Blackpearl service is restarted. This happens even if you specifiy the Zone in ZoneCalculateEvent.