When automatic resiizng via ContentSizeFitter proves insufficient, manual calculation of text dimensions becomes necessary. Force layout updates using LayoutRebuilder.ForceRebuildLayoutImmediate() when required.

using TMPro;
using UnityEngine;

public static class TMPDimensionUtility
{
    public static Vector2 ConstrainToWidth(this TextMeshProUGUI tmpComponent, string content, float maxWidth)
    {
        Vector2 computedSize = tmpComponent.GetPreferredValues(content, maxWidth, 0);
        tmpComponent.rectTransform.SetSizeWithCurrentAnchors(RectTransform.Axis.Horizontal, maxWidth);
        tmpComponent.rectTransform.SetSizeWithCurrentAnchors(RectTransform.Axis.Vertical, computedSize.y);
        tmpComponent.text = content;
        return new Vector2(maxWidth, computedSize.y);
    }

    public static Vector2 ConstrainToHeight(this TextMeshProUGUI tmpComponent, string content, float maxHeight)
    {
        Vector2 computedSize = tmpComponent.GetPreferredValues(content, 0, maxHeight);
        tmpComponent.rectTransform.SetSizeWithCurrentAnchors(RectTransform.Axis.Horizontal, computedSize.x);
        tmpComponent.rectTransform.SetSizeWithCurrentAnchors(RectTransform.Axis.Vertical, maxHeight);
        tmpComponent.text = content;
        return new Vector2(computedSize.x, maxHeight);
    }
}

Usage example:

using TMPro;
using UnityEngine;

public class DimensionConstraintDemo : MonoBehaviour
{
    public TextMeshProUGUI displayText;

    [TextArea(5, 15)]
    public string sampleContent;

    public float widthLimit;
    public float heightLimit;

    void Update()
    {
        if (Input.GetKeyDown(KeyCode.Space))
        {
            displayText.ConstrainToWidth(sampleContent, widthLimit);
        }
        if (Input.GetKeyDown(KeyCode.A))
        {
            displayText.ConstrainToHeight(sampleContent, heightLimit);
        }
    }
}