In the context of sketch planning, a simplified network (i.e., an abstract network or subnetwork) model is expected to accurately approximate travel demand patterns and level-of-service attributes obtained from its full-network counterpart. A data prerequisite in this approximation process is the trip matrix of the simplified network. This paper discusses a maximum entropy method for the subnetwork trip matrix estimation problem, relying only on link flow rates estimated with the use of full-network traffic assignment or as observed link-level vehicle counts. A linearization algorithm of the Frank-Wolfe type is devised for problem solutions in which a column-generation approach is used iteratively to solve the linearized subproblem without path enumeration. Encouraging results from sample applications of different size and topology suggest that this method holds much promise for generating trip matrices that can be used to evaluate traffic flow patterns under various network changes.