Micro well-plates are an apparatus commonly used in chemical and biological experiments that are a few centimeters thick and contain wells or divets. In this paper, we aim to solve the task of placing the well-plate onto a well-plate holder (referred to as holder). This task is challenging due to the holder's raised grooves being a few millimeters in height, with a clearance of less than 1 mm between the well-plate and holder, thus requiring precise control during placing. Our placing task has the following challenges: 1) The holder's detected pose is uncertain; 2) the required accuracy is at the millimeter to sub-millimeter level due to the raised groove's shallow height and small clearance; 3) the holder is not fixed to a desk and is susceptible to movement from external forces. To address these challenges, we developed methods including a) using tactile sensors for accurate pose estimation of the grasped well-plate to handle issue (1); b) sliding the well-plate onto the target holder while maintaining contact with the holder's groove and estimating its orientation for accurate alignment. This allows for high precision control (addressing issue (2)) and prevents displacement of the holder during placement (addressing issue (3)). We demonstrate a high success rate for the well-plate placing task, even under noisy observation of the holder's pose.