In such a code:

if (insuranceNumberSearch == null
     ? true
     : ei.InsuranceNumber.Contains(insuranceNumberSearch.Trim()))
   doSomething();

where insuranceNumberSearch is null, remaining expression is not null while in following code:

var q = from ei in session.Linq<EmployeeInsurance>()
        where insuranceNumberSearch == null
                ? true
                : ei.InsuranceNumber.Contains(insuranceNumberSearch.Trim())
        select ei;

all section of expression is evaluated regardless of insuranceNumberSearch is null or is not null.

I'm using LINQ to NHibernate

UPDATE:

Unfortunately I have put the first snippet wrong. The correct is:

if (insuranceNumberSearch == null || (insuranceNumberSearch != null && ei.InsuranceNumber.Contains(insuranceNumberSearch.Trim()))
doSomething();

bool b1 = insuranceNumberSearch == null ? true : ei.InsuranceNumber.Contains(insuranceNumberSearch.Trim());
if (b1)
doSomething();

In both of above when insuranceNumberSearch is null, remaining expressions are not evaluated any more. If such a behavior does not exists, insuranceNumberSearch.Trim() will cause a reference object is null exception. Sadly LINQ (or maybe LINQ-to-NHibernate) does not obey such a nice behavior and evaluate all of expression even when insuranceNumberSearch is null and results in error.

UPDATE 2: I found a similar question: The || (or) Operator in Linq with C#

Beat me, but wth wouldn't you use

if (
     (insuranceNumberSearch == null) ||
     ei.InsuranceNumber.Contains(insuranceNumberSearch.Trim()))
  doSomething();

in your statement, be it in the LINQ expression or not?