How to stop your opponent breaking your grip
Many techniques in aikido require a non-slip grip on uke's wrist. In particular gokyo (fifth pin) and shiho-nage are techniques in which uke's arm has a natural tendency to twist in (and indeed out of) tori's grip.
Having a firm grip is not a matter of grip strength. Indeed the feeling of the grip should be like that of a new born baby grasping an adult's thumb. Preventing an uke from twisting out of a grip is a matter of friction and leverage rather than strength.
A typical western style grip probably accentuates the role of the thumb and the directly opposing index finger. This creates a relatively small fulcrum which means that the arm being gripped has an easier task of applying leverage against the grip. An aikido grip by contrast accentuates the thumb and the three smaller fingers and this potentially engages the whole of the palm. In fact the index finger may be entirely disengaged. The grip is therefore achieved through the full width of the hand. This allows a considerable amount of frictional force to be applied with relatively little effort, making it difficult for the gripped wrist to rotate against the hold. The fulcrum of the grip is also the entire width of the palm, rather than the narrow joint between thumb and index finger, making it more difficult to apply leverage against the grip.
To make the grip more effective one should target the base of the gripped person's hand rather than just their wrist. Being roughly circular the wrist can more easily twist. However the base of the hand has a flatter profile and when closely held by the flat of the enclosing palm this provides a natural lock.
Finally the grip is normally applied top down (palm on top, thumb underneath) regardless of whether uke's arm is palm up or palm down. Gripping from underneath the arm (thumb on top) allows uke to use the biceps easily against the gripping thumb. However a grip with the thumb underneath means that uke has to use a weaker muscles against the thumb simply because of the anatomy of the arm. Pictures below show the correct grip for a shiho-nage technique.
Good extension of uke's arm is also important. If it is stretched out uke's posture is compromised and they are less able to retrieve their arm or their posture.