Advance in computational rheology allows for in silico predictions of the viscoelastic responses of arbitrarily branched polymer melts. While detailed branching structure is required for the rheology predictions, rheology itself is often the most sensitive tool to detect low levels of branching. With rheological experiments and computational modeling of a set of nominally linear and model comb ethylene-butene copolymers, we show that coupled models for the synthesis and rheology can integrate diverse measurements, incorporating inherent experimental uncertainties. This approach allows us to achieve tight bounds on the branching structures of the constituent molecules. Next, we numerically explore the effects of the numbers and molar masses of side arms in comb polymers on the viscoelastic responses in both the linear and nonlinear regimes. Such computational exploration can aid in designing specific polymers suitable for a given processing scenario.