Currently, over forty transiting planets have been discovered by ground-based photometric surveys, and space-based missions like Kepler and CoRoT are expected to detect hundreds more. Follow-up photometric observations from the ground will play an important role in constraining both orbital and physical parameters for newly discovered planets, especially those with small radii (R_p less than approximately 4 Earth radii) and/or intermediate to long orbital periods (P greater than approximately 30 days). Here, we simulate transit light curves from Kepler-like photometry and ground-based observations in the near-infrared (NIR) to determine how jointly modeling space-based and ground-based light curves can improve measurements of the transit duration and planet-star radius ratio. We find that adding observations of at least one ground-based transit to space-based observations can significantly improve the accuracy for measuring the transit duration and planet-star radius ratio of small planets (R_p less than approximately 4 Earth radii) in long-period (~1 year) orbits, largely thanks to the reduced effect of limb darkening in the NIR. We also demonstrate that multiple ground-based observations are needed to gain a substantial improvement in the measurement accuracy for small planets with short orbital periods (~3 days). Finally, we consider the role that higher ground-based precisions will play in constraining parameter measurements for typical Kepler targets. Our results can help inform the priorities of transit follow-up programs (including both primary and secondary transit of planets discovered with Kepler and CoRoT), leading to improved constraints for transit durations, planet sizes, and orbital eccentricities.